Probably the DVDs meant for teaching babies use signs that are simpler to do-- I'm not sure with what words you've noticed the discrepancy, but if there are two ways of signing something, the baby DVDs will use the one that is easier for the little ones to sign.

Since you've looked up some websites too, you may be familiar with the "ASL University" one, but I'll put the link here because it's the best sign language site I've seen. If you see it on here you can trust that it's correct:

http://www.lifeprint.com/