user137: All these 3 philosophy/religions are born across Tibet/Nepal/India and they all share numerous concept and practice.
Some points of connections could be:

Noble Eightfold Path are very similar to Yamas in Yoga
Concept of Reincarnation
Karma
Meditation approach as technique to reach enlightenment  
Meditation positions: actually the lotus posture, usually used in Buddish for meditation, is a yoga asana
Yantra
Mudras

More in general:

Hinduism and Yoga are almost on the same line, they born in the same time and are based on same concepts.
Buddhism, instead is more "modern", Buddha is dated between 563 BCE to 483, Hinduism/Yoga are thousand of years older, and in someway it is a consequence of the first two:
it is born in an environment where Hinduism/Yoga concept were the basement of the culture.

One of the main difference is:

Buddhism doesn't speak about God but speak about "life and how to live" or better how to stop to suffer. ( so it is basically the oldest psychoanalytic method known )  

Personally I believe that the reason behind this (non speaking about God) is because Buddha is like saying "Before speaking about God, you need to be ready and stable and find your self" or better "you don't need to speak about God, you have to find it and the shorter and safer path is inside you."
Main Point of the question:
Define a relationship between the above entities as they are strictly related and so point out the elements of difference that Buddhism philosophy introduces.
I think that this can be helpful to anyone that is approaching to Buddhism.

user10200: We cannot find truth by studying and making comparisons among those so called scriptures of different theories time experienced , we have to experience our own doubts with humble and gentle    self precipitation, which needs very innocent and Self ignited mind , as an individual entity.

user111: Not too sure about Yoga. But I believe the core teachings of Hinduism are based on Nithya, Sukha, Athma. Which is the exact opposite of Buddhist teachings. So they are fundamentally very different. Hinduism is much more similar to Christianity and Islam at the core. Just that Christians and Muslims believe in one almighty God/Allah who takes care of everything, whereas in Hinduism the powers are distributed among at least 3 Gods: Maha brahma, Shiva, Vishnu.

user208: You have tried to show the similarities between Hinduism and Buddhism (i am not talking about Yoga as I have not studied it much comparing to other two subjects. And also because I am doubtful about if it can considered as separated philosophy or religion.). In doing that you have talked about time period ( and similarities due to that) and about philosophical similarities - similarities in teaching. 
In case of similarities of teaching we need to be little careful. There can be confusion due similarities of words. I will give just one eg. - you have talked about Karma. But Karma in Buddhism and Karma in Hinduism is very different. Plz refer to Buddha and His Dhamma. 
In case of time period you are in other words saying that Buddhism is nothing but something build ed up on Hinduism. Again I have some doubts. This is mainly due the reason that Hinduism as such is very modern concept. There was Vedic time. But at that time various other philosophies were also present which were not strictly Vedic. And yes, as far as I understand Buddha derived lot from them as he was master in all those philosophies. It is surely different from considering Hinduism as base of Buddhism. 
In case of differences, yes differences regarding presence of God are true. But we can not miss a major difference - Hinduism is highly dependent up on Varna system where as in Buddhism there is no such system, in fact, Buddhism is against any such system of gradation. 
With all this, I have expressed my concerns regarding mixing Buddhism with Hinduism or reverse or saying that they are on same lines. For me Buddhism shares adverse relationship with Hinduism. It it the great religion of "Maitri" which is against any division between human beings on the basis of there birth. It is this aspect that a person who is approaching to Buddhism (especially from Hindu fold) should know. 
Thankful to you for raising such important topic that helped me to express. Looking forward for further discussion on the points I have mentioned. 

user16: Now this answer is about the historical development of Buddhism. In the mid of the last millenium BC there was a general movement in India, the so called Śramaṇa-movement. Cp. http://en.wikipedia.org/wiki/Sramana
It was an ascetic movement whose adherents strove to find liberation from this world and the cycle of rebirths by themselves and aside from the Vedic-brahmanic religion of sacrifice. The first literary witnesses of this movement are certain Upaniṣads, some of which the Buddha was also taught by the two teachers mentioned in the canon. One of the most important literary witnesses is the Sāmaññaphalasutta of the Pali canon.
A lot, actually most of the philosophical base of Buddhism was common sense of this movement. Even such a "totally Buddhist" doctrine as the Pratityasamutpada springs from this common source as can be shown by parallel structures (far less important and far less developed) in the Jaina canon and in the Manu-Bṛhaspati-Saṃvāda in the Mahabharata epic.
Now, to answer the question, apart from the person of the Buddha, there is IMO just one thing which singles out Buddhism as a movement of its own from the common ground of the Śramaṇas and that is precisely the theory of anattā or anātman. Up to the "mahayanic revolution" each and every philosophical development in Buddhism is already foreshadowed by this theory and these developments can quite consistently be seen as a fathoming of the hidden implications of that single tenet.
A note on dates:

It is quite well agreed that the oldest portions of the Vedic Literature are not older than 2000 BC or 1800 BC, rather younger.
The first Upanishads date from not before 800 BC, rather starting from around 600 BC
The Buddhas Parinirvana took place somewhen between 545 BC and 400 BC
Patanjalis Yoga-Sutras cannot reliably be dated, but it is unlikely, he lived before the second century BC

This makes Yoga younger than Buddhism.
Now, this was for the time, when Buddhism first developed. Until the time, that Buddhism nearly completely vanished from the scene in India, there were of course various influences from and to Buddhism, as has been pointed out in other answers.

user82: In Buddhism God is irrelevant. His existence or non existence doesn't affect the suffering that a being experiences here. Suffering is the problem that is caused by desire and attachment. Mind being the place where suffering is experienced, both Buddhism and Hinduism give the solution of controlling the mind through meditation to get rid of suffering and mental afflictions.
Yoga is just a process of ceasing the mental activities (yogaḥ citta-vṛtti nirodha - patnjali yoga sutra 1.2). It is only when the mind is active and thinking that any  feeling of joy or suffering arises. So through yoga and meditation the objective of calming and stilling the mind is achieved. Although Yoga was developed and preached by Vedic (Hindu) sages like Patanjali, it being just a physical process also practiced by Buddhists, just like we use cars or computers developed by scientists of other religion.
If you want a historical chronology then undoubtedly you can place Yoga system of Hinduism ahead of Buddhism. If you go through Vedic texts like Upanishads and Gita, which were available before the formation of Buddhism, then you will find mention of Yoga, meditation and other related practices. But in course of time both have influenced one another.
Regarding the relation between Buddhism and Hinduism my personal belief is Buddhism is Hinduism unnecessary parts casted out. While Buddishm primarily focuses on making life free of suffering here in the present life, Hinduism takes into account both here and the hereafter. Hence, while there are many yanjya and sacrifices prescribed in the Vedic religion for the hereafter, there are none such in Buddhism. The Upanishadic portions of the Vedas has teachings that are to some extent similar to the teachings of Buddhism. Both prescribe meditation as the mean to attain liberation. In fact message of Upanishads, Gita and other Vedic scriptures state that one who desires real benefit should not pursue sacrifices, yanjya, etc. as they provide temporary fruits in the after life and doesn't offer permanent liberation from material existence.
So the point is Yoga not being a philosophy (about which people can have different opinions) but being a physical solution to the problem of suffering is common and practiced both by followers of Hinduism and Buddhism. However, the point to note is that basically the meditation portion of Yoga are practiced by both, not the yoga asans or postures. Yoga postures and asanas are primarily practiced in Hata Yoga system which belongs to Hinduism.

user135: Hinduism & Yoga aren't 2 different things. They are the same. 
Yoga is one of the 6 main Darshanas of Hinduism. I.e it provides it's own path for liberation. Other Darshanas(Advaita, etc) too use Yoga as a valid means but not the only valid means. 
Can't really say Buddhism is modern. It evolved along with Yoga both of which can be traced to around 4th century BCE. 
Both Hindu Darshanas & Buddhism evolved influencing each other. For example Advaita borrowed some of it's elements from Nagarjuna. Tibetan Buddhism incorporated Tantra which is considered 'Hindu'. 
Tibetan Buddhism has it's own version of Yoga called Trul khor.
Hence to answer your question, they all belong to the same family, the Dharmic family and have influenced each other.

137: <p>All these 3 philosophy/religions are born across Tibet/Nepal/India and they all share numerous concept and practice.</p>

<p>Some points of connections could be:</p>

<ul>
<li>Noble Eightfold Path are very similar to Yamas in Yoga</li>
<li>Concept of Reincarnation</li>
<li>Karma</li>
<li>Meditation approach as technique to reach enlightenment  </li>
<li>Meditation positions: actually the lotus posture, usually used in Buddish for meditation, is a yoga asana</li>
<li>Yantra</li>
<li>Mudras</li>
</ul>

<p>More in general:</p>

<ul>
<li>Hinduism and Yoga are almost on the same line, they born in the same time and are based on same concepts.</li>
<li>Buddhism, instead is more "modern", Buddha is dated between 563 BCE to 483, Hinduism/Yoga are thousand of years older, and in someway it is a consequence of the first two:
it is born in an environment where Hinduism/Yoga concept were the basement of the culture.</li>
</ul>

<p>One of the main difference is:</p>

<ul>
<li>Buddhism doesn't speak about God but speak about "life and how to live" or better how to stop to suffer. ( so it is basically the oldest psychoanalytic method known )  </li>
</ul>

<p>Personally I believe that the reason behind this (non speaking about God) is because Buddha is like saying "Before speaking about God, you need to be ready and stable and find your self" or better "you don't need to speak about God, you have to find it and the shorter and safer path is inside you."</p>

<p><strong>Main Point of the question:</strong><br>
Define a relationship between the above entities as they are strictly related and so point out the elements of difference that Buddhism philosophy introduces.</p>

<p>I think that this can be helpful to anyone that is approaching to Buddhism.</p>
 10200: <p>We cannot find truth by studying and making comparisons among those so called scriptures of different theories time experienced , we have to experience our own doubts with humble and gentle    self precipitation, which needs very innocent and Self ignited mind , as an individual entity.</p>
 111: <p>Not too sure about Yoga. But I believe the core teachings of Hinduism are based on Nithya, Sukha, Athma. Which is the exact opposite of Buddhist teachings. So they are fundamentally very different. Hinduism is much more similar to Christianity and Islam at the core. Just that Christians and Muslims believe in one almighty God/Allah who takes care of everything, whereas in Hinduism the powers are distributed among at least 3 Gods: Maha brahma, Shiva, Vishnu.</p>
 208: <p>You have tried to show the similarities between Hinduism and Buddhism (i am not talking about Yoga as I have not studied it much comparing to other two subjects. And also because I am doubtful about if it can considered as separated philosophy or religion.). In doing that you have talked about time period ( and similarities due to that) and about philosophical similarities - similarities in teaching. </p>

<p>In case of similarities of teaching we need to be little careful. There can be confusion due similarities of words. I will give just one eg. - you have talked about Karma. But Karma in Buddhism and Karma in Hinduism is very different. <a href="http://www.columbia.edu/itc/mealac/pritchett/00ambedkar/ambedkar_buddha/04_02.html#02_01" rel="nofollow">Plz refer to Buddha and His Dhamma</a>. </p>

<p>In case of time period you are in other words saying that Buddhism is nothing but something build ed up on Hinduism. Again I have some doubts. This is mainly due the reason that Hinduism as such is very modern concept. There was Vedic time. But at that time various other philosophies were also present which were not strictly Vedic. And yes, as far as I understand Buddha derived lot from them as he was master in all those philosophies. It is surely different from considering Hinduism as base of Buddhism. </p>

<p>In case of differences, yes differences regarding presence of God are true. But we can not miss a major difference - Hinduism is highly dependent up on Varna system where as in Buddhism there is no such system, in fact, Buddhism is against any such system of gradation. </p>

<p>With all this, I have expressed my concerns regarding mixing Buddhism with Hinduism or reverse or saying that they are on same lines. For me Buddhism shares adverse relationship with Hinduism. It it the great religion of "<em>Maitri</em>" which is against any division between human beings on the basis of there birth. It is this aspect that a person who is approaching to Buddhism (especially from Hindu fold) should know. </p>

<p>Thankful to you for raising such important topic that helped me to express. Looking forward for further discussion on the points I have mentioned. </p>
 16: <p>Now this answer is about the historical development of Buddhism. In the mid of the last millenium BC there was a general movement in India, the so called <em>Śramaṇa</em>-movement. Cp. <a href="http://en.wikipedia.org/wiki/Sramana" rel="noreferrer">http://en.wikipedia.org/wiki/Sramana</a></p>

<p>It was an ascetic movement whose adherents strove to find liberation from this world and the cycle of rebirths by themselves and aside from the Vedic-brahmanic religion of sacrifice. The first literary witnesses of this movement are certain <em>Upaniṣads</em>, some of which the Buddha was also taught by the two teachers mentioned in the canon. One of the most important literary witnesses is the <em>Sāmaññaphalasutta</em> of the Pali canon.</p>

<p>A lot, actually most of the philosophical base of Buddhism was common sense of this movement. Even such a "totally Buddhist" doctrine as the Pratityasamutpada springs from this common source as can be shown by parallel structures (far less important and far less developed) in the Jaina canon and in the <em>Manu-Bṛhaspati-Saṃvāda</em> in the Mahabharata epic.</p>

<p>Now, to answer the question, apart from the person of the Buddha, there is IMO just one thing which singles out Buddhism as a movement of its own from the common ground of the <em>Śramaṇas</em> and that is precisely the theory of <em>anattā</em> or <em>anātman</em>. Up to the "mahayanic revolution" each and every philosophical development in Buddhism is already foreshadowed by this theory and these developments can quite consistently be seen as a fathoming of the hidden implications of that single tenet.</p>

<p>A note on dates:</p>

<ul>
<li>It is quite well agreed that the oldest portions of the Vedic Literature are not older than 2000 BC or 1800 BC, rather younger.</li>
<li>The first Upanishads date from not before 800 BC, rather starting from around 600 BC</li>
<li>The Buddhas Parinirvana took place somewhen between 545 BC and 400 BC</li>
<li>Patanjalis Yoga-Sutras cannot reliably be dated, but it is unlikely, he lived before the second century BC</li>
</ul>

<p>This makes Yoga younger than Buddhism.</p>

<p>Now, this was for the time, when Buddhism first developed. Until the time, that Buddhism nearly completely vanished from the scene in India, there were of course various influences from and to Buddhism, as has been pointed out in other answers.</p>
 82: <p>In Buddhism God is irrelevant. His existence or non existence doesn't affect the suffering that a being experiences here. Suffering is the problem that is caused by desire and attachment. Mind being the place where suffering is experienced, both Buddhism and Hinduism give the solution of controlling the mind through meditation to get rid of suffering and mental afflictions.</p>

<p>Yoga is just a process of ceasing the mental activities (<em>yogaḥ citta-vṛtti nirodha</em> - patnjali yoga sutra 1.2). It is only when the mind is active and thinking that any  feeling of joy or suffering arises. So through yoga and meditation the objective of calming and stilling the mind is achieved. Although Yoga was developed and preached by Vedic (Hindu) sages like Patanjali, it being just a physical process also practiced by Buddhists, just like we use cars or computers developed by scientists of other religion.</p>

<p>If you want a historical chronology then undoubtedly you can place Yoga system of Hinduism ahead of Buddhism. If you go through Vedic texts like Upanishads and Gita, which were available before the formation of Buddhism, then you will find mention of Yoga, meditation and other related practices. But in course of time both have influenced one another.</p>

<p>Regarding the relation between Buddhism and Hinduism my personal belief is Buddhism is Hinduism unnecessary parts casted out. While Buddishm primarily focuses on making life free of suffering here in the present life, Hinduism takes into account both here and the hereafter. Hence, while there are many <em>yanjya</em> and sacrifices prescribed in the Vedic religion for the hereafter, there are none such in Buddhism. The Upanishadic portions of the Vedas has teachings that are to some extent similar to the teachings of Buddhism. Both prescribe meditation as the mean to attain liberation. In fact message of Upanishads, Gita and other Vedic scriptures state that one who desires real benefit should not pursue sacrifices, <em>yanjya</em>, etc. as they provide temporary fruits in the after life and doesn't offer permanent liberation from material existence.</p>

<p>So the point is Yoga not being a philosophy (about which people can have different opinions) but being a physical solution to the problem of suffering is common and practiced both by followers of Hinduism and Buddhism. However, the point to note is that basically the meditation portion of Yoga are practiced by both, not the yoga <em>asans</em> or postures. Yoga postures and <em>asanas</em> are primarily practiced in Hata Yoga system which belongs to Hinduism.</p>
 135: <p>Hinduism &amp; Yoga aren't 2 different things. They are the same. 
Yoga is one of the 6 main Darshanas of Hinduism. I.e it provides it's own path for liberation. Other Darshanas(Advaita, etc) too use Yoga as a valid means but not the only valid means. </p>

<p>Can't really say Buddhism is modern. It evolved along with Yoga both of which can be traced to around 4th century BCE. </p>

<p>Both Hindu Darshanas &amp; Buddhism evolved influencing each other. For example Advaita borrowed some of it's elements from Nagarjuna. Tibetan Buddhism incorporated Tantra which is considered 'Hindu'. </p>

<p>Tibetan Buddhism has it's own version of Yoga called <a href="http://en.wikipedia.org/wiki/Trul_khor">Trul khor</a>.</p>

<p>Hence to answer your question, they all belong to the same family, the Dharmic family and have influenced each other.</p>
