user116: I have seen Buddha statues in western pop culture that portray an obese man as the Buddha. During my experience with Buddhism I have seen many more statues of the Buddha as a slim man, usually with one hand up, palm out.
Two pictures to illustrate:
Western pop culture portrayal:

More typical eastern portrayal:


I seek an explanation as to the reason for the difference in portrayal, if they are even of the same person.

user92: 
Budai or Pu-Tai (Chinese: 布袋; pinyin: Bùdài), or Hotei in Japanese, Bố
  Đại in Vietnamese, is a Chinese folkloric deity. His name means "Cloth
  Sack," and comes from the bag that he is conventionally depicted as
  carrying. He is usually identified with or seen as an incarnation of
  Maitreya, the future Buddha, so much so that the Budai image is one of
  the main forms in which Maitreya is depicted in East Asia. He is
  almost always shown smiling or laughing, hence his nickname in
  Chinese, the Laughing Buddha (Chinese: 笑佛). Many people in the West
  mistake the image of Budai as being Gautama Buddha.
  -Budai from Wikipedia

So as it seems, it's a misattribution of western culture.  
Top one is Budai, the bottom one is Gotama Buddha. But the bottom one is also depicted incorrectly, since the Pāḷi Canon portrays the Buddha as bald (muṇḍaka, "bald-shaven man").

user179: I second the answers already given;
As with many other spiritual teachers, I.E.: Jesus, Mohammed. No resemblance was made during their lifetime. According to some sources the first statues where made in the first century and second century in what is now called Afghanistan and Pakistan. So nobody really knows what he looked like. 
Source: http://www.buddhanet.net/e-learning/dharmadata/fdd35.htm
According to the same site, the sitting version of the statue (the second one you posted), was meant to resemble a bodhisattva called: "Maitreya" and not necessarily Siddhartha Gautama
Source: http://www.buddhanet.net/e-learning/dharmadata/fdd28.htm
Lastly I want to add that the Buddha has also been incorporated within Hinduism, as one of the reincarnations of Vishnu. So some of the visual representations of the Buddha or not Buddhist at all.
Source: http://en.wikipedia.org/wiki/Gautama_Buddha_in_Hinduism

user253: The first statue is not Gautama Buddha (commonly referred to as "the Buddha"), but is Budai, a depiction of a loving and jovial Chinese monk, who is often considered a depiction of Maitreya, the next Buddha who will come into the world eons from now. 
Even some of the "skinny" Buddha statues may or may not be an image of Gautama Buddha. It mostly depends on the mudras (position of the hands) and the symbols used in the depiction. For example, usually Gautama Buddha has at least one palm facing inward with his fingers pointed towards the ground, but often today, commercialized statues sold in the west depict him in any kind of way because they do not understand the mudras and symbolism.

116: <p>I have seen Buddha statues in western pop culture that portray an obese man as the Buddha. During my experience with Buddhism I have seen many more statues of the Buddha as a slim man, usually with one hand up, palm out.</p>

<p><strong>Two pictures to illustrate:</strong></p>

<p><strong>Western pop culture portrayal:</strong></p>

<p><img src="https://i.stack.imgur.com/m8QQK.jpg" alt="Popular Culture portrayal of Buddha statue"></p>

<p><strong>More typical eastern portrayal:</strong></p>

<p><img src="https://i.stack.imgur.com/lfBr5.png" alt="Eastern portrayal of Buddha statue"></p>

<hr>

<p>I seek an explanation as to the reason for the difference in portrayal, if they are even of the same person.</p>
 92: <blockquote>
  <p><em>Budai</em> or <em>Pu-Tai</em> (Chinese: 布袋; pinyin: Bùdài), or <em>Hotei</em> in Japanese, <em>Bố
  Đại</em> in Vietnamese, is a Chinese folkloric deity. His name means "Cloth
  Sack," and comes from the bag that he is conventionally depicted as
  carrying. He is usually identified with or seen as an incarnation of
  <em>Maitreya</em>, the future <em>Buddha</em>, so much so that the <em>Budai</em> image is one of
  the main forms in which <em>Maitreya</em> is depicted in East Asia. He is
  almost always shown smiling or laughing, hence his nickname in
  Chinese, the <em>Laughing Buddha</em> (Chinese: 笑佛). <strong>Many people in the West
  mistake the image of Budai as being Gautama Buddha.</strong><br>
  -<em><a href="http://en.wikipedia.org/wiki/Budai" rel="nofollow">Budai</a> from Wikipedia</em></p>
</blockquote>

<p>So as it seems, it's a misattribution of western culture.  </p>

<p>Top one is <em>Budai</em>, the bottom one is <em>Gotama Buddha</em>. But the bottom one is also depicted incorrectly, since the <a href="http://en.wikipedia.org/wiki/P%C4%81li_Canon" rel="nofollow"><em>Pāḷi Canon</em></a> portrays the <em>Buddha</em> as <a href="http://asiapacific.anu.edu.au/newmandala/2010/12/30/the-buddha-was-bald/" rel="nofollow">bald</a> (<em>muṇḍaka</em>, "bald-shaven man").</p>
 179: <p>I second the answers already given;</p>

<p>As with many other spiritual teachers, I.E.: Jesus, Mohammed. No resemblance was made during their lifetime. According to some sources the first statues where made in the first century and second century in what is now called Afghanistan and Pakistan. So nobody really knows what he looked like. </p>

<p>Source: <a href="http://www.buddhanet.net/e-learning/dharmadata/fdd35.htm" rel="nofollow">http://www.buddhanet.net/e-learning/dharmadata/fdd35.htm</a></p>

<p>According to the same site, the sitting version of the statue (the second one you posted), was meant to resemble a bodhisattva called: "Maitreya" and not necessarily Siddhartha Gautama</p>

<p>Source: <a href="http://www.buddhanet.net/e-learning/dharmadata/fdd28.htm" rel="nofollow">http://www.buddhanet.net/e-learning/dharmadata/fdd28.htm</a></p>

<p>Lastly I want to add that the Buddha has also been incorporated within Hinduism, as one of the reincarnations of Vishnu. So some of the visual representations of the Buddha or not Buddhist at all.</p>

<p>Source: <a href="http://en.wikipedia.org/wiki/Gautama_Buddha_in_Hinduism" rel="nofollow">http://en.wikipedia.org/wiki/Gautama_Buddha_in_Hinduism</a></p>
 253: <p>The first statue is not Gautama Buddha (commonly referred to as "the Buddha"), but is Budai, a depiction of a loving and jovial Chinese monk, who is often considered a depiction of Maitreya, the next Buddha who will come into the world eons from now. </p>

<p>Even some of the "skinny" Buddha statues may or may not be an image of Gautama Buddha. It mostly depends on the mudras (position of the hands) and the symbols used in the depiction. For example, usually Gautama Buddha has at least one palm facing inward with his fingers pointed towards the ground, but often today, commercialized statues sold in the west depict him in any kind of way because they do not understand the mudras and symbolism.</p>
