I see all this talk about H4, H3, H7, etc and 9004, 9003.
Are these different names for a similar bulb? like... is the H4 and 9004 the same or totally different bulbs? I have a hard time finding H4 bulbs at auto stores... but 9004's and the likes are plenty.

H4 bulbs are also commonly referred to as 9003 and HB2. Rest assured, they are all the same thing.