What are the different types of yoga and what are the differences?

If you mean only styles of Hatha yoga -- practices where physical postures ("asana") are a main component (in the West, sometimes the only), following is a fairly good list (but by no means complete; I've never come across a list that claims to be complete):

http://www.traditionalyogastudies.com/wp-content/u...

If you mean yoga in the broadest sense (more than just union of physical body and mind; "the realization in direct experience of the preexisting union between the individual consciousness and the universal consciousness"), then following site is a good place to start:

http://www.swamij.com/yoga.htm

Namaste',

dwb