Q:

What is a different between different kind of pushup workout?

I want to know there is number of variety pushup styles.

Traditional pushup
Wide-grip pushup
Close-grip pushup
Clap pushup
One-leg pushup
Dead-stop pushup
Eccentric pushup
Spider-Man pushup
One-armed incline pushup
Decline pushup
Incline pushup

Please explain what is different between each pushups and how it is effect for body?

A:

Traditional pushup 
I think you mean a push up with elbows sliding down and up your torso, this one uses the most muscles in your body. If you do this exercise weighted either with a dipping belt/rope, with bands or with plates on your back you can also get a good Gluteus and calf exercise out of it. 
Wide grip pushups
Pushing with your elbows parallel to your feet in order to make a T is probably going to seriously damage your shoulder.
Try raising your arms in a T position while standing, then push forward while bending your elbows, you will notice your shoulders being rotated and rounded forward and downward. This is one of the weakest position for your ligaments and tendons on the shoulder, avoid it to avoid injuries.
Close grip pushups
This one puts the Pectoralis major in a  really disadvantageous position letting all the work to the Pectoralis minor,Trapizius,Serratus anterior,Rhomboid,Deltoid and Tricep. 
This one is quite good if you want to overload those muscles while sacrificing a bit of chest size. 
Clapping pushup 
Good exercise for cardio and explosiveness. One of the most functional exercise that carry over to sports and martial arts. 
Mix it with some clapping inverted rows, and jumping air squats to get one of the most effective cardio workout. 
You can also do it each morning as daily conditioning to start your day. It might also save your heart over the long run. 
One legged pushup
This is pretty much just a normal push up that requires a little bit more stabilization and is kind of ''heavier'' while building some endurance in the Gluteus. 
Deadstop pushup
This eliminates elasticity and forces the body to become stronger in it's weakest positions. It's one of these exercises where you will get stronger faster than you build muscle, like the deadlift for example. 
Eccentric pushup
This is bodybuilding move, quite the opposite of deadstop.
Muscles are like bands, they are going to be damaged during the stretched position not the contracted one or at least not as much.
Eccentric exercises are overall good to build muscle and endurance when you don't really care that much about strength.
Spiderman pushup
This is a better version of the one legged push up as it puts even more weight on your upper body and uses some lower oblique. 
I actually did built my Adonis Belt by doing spiderman push ups with resistance bands on my legs, when I pull the leg up to my chest or out to my elbow I also pull the band and get some resistance. In theory this exercise has infinite loading potential because you can use as many bands as you can afford. 
One arm pushup and inclined pushup 
Like any unilateral exercise it's good to fix imbalances  while also giving some passive work to the muscles on the sides of your core like the Quadratus Lumborum and the Oblique muscles. 
Also, progressive angulation is a good way to get stronger. 
Starting from an high incline you can increase the angle more and more until you are able to do it 180° on the ground. 
Decline pushup 
This might or might not carry over to the overhead press or the handstand push up depending and the width of your torso and the length of your arms because strength is joint to angle specific.
And also eliminates some work from the chest and overloads the Trapezius muscles and the long head of the Tricep while also putting some more emphasis on the frontal Deltoid, even more than the close grip pushup. 

