Vet wrap is used with gauze for doing wound dressings. I also use my vet wrap on my legs when I forget to wear socks that cover my ankle. http://www.coldwrap.com/images/leg2.jpg
Pillows, leg quilts, standing bandages, stall bandages, are all the same. They support the leg and prevent inflammation. So after a hard work out before putting your horse in it's stall you would put these wraps on. http://www.millcrossing.com/images/wrap2_small.jpg
Polo wraps and track bandages are for exercising. They support the leg and give a small amount of protection. http://www.theequinest.com/images/polo-wrap.jpg
Cotton would be used for wound dressings or it could be used to make a cloth in a shipping bandage. I can't find a picture for a shipping bandage but it's like a stable wrap that goes all the way from the bulbs of the heel to halfway up the knee or hock.
Standing wraps would be good to use for your horse. But learn how to do them correctly or you can bow his tendon and cause discomfort.
Edit: Sorry, those were the best pictures I could find after looking through page after page in google images!
Here's videos.
Polo - http://www.ehow.com/video_2350426_wrap-rodeo-horses-legs.html
Vet wrap - http://video.google.com/videoplay?docid=4196694922737064951&ei=oYEkS8_BFIP0qAOqx6nFAQ&q=vet+wrap+horse&hl=en&client=firefox-a#
Standing - http://www.youtube.com/watch?v=eMUz_zVqGGU