As I understand them...
Hopbursting generally refers to more or less continuously adding hops during your boil.
Brew water hops I don't have a clue.
Mash hops are just that, hops that you add to the mash.
First wort hops are the hops that you drop into your kettle and then drain/sparge the wort right on top of them.
Boil hops would seem pretty self explanatory
Hopback hops refers to when you're transferring out of the kettle after the boil, the wort gets run through hops contained in a "hopback".