... Actually goth is considered a lifestyle, unless you mean mallgoths, which are those obnoxious HotTopic kiRAB who worship Slipknot and wear nothing but Tripp pants. But both goth and punk were originally subcultures in the 70's and 80's.
Basically emo used to be a genre of music, but then somehow became a style branched off the mallgoth. Basically seen as kiRAB with eyeliner, listening to stuff like MCR, hair in face, etc.
Because the emo stereotype (Which I hate to say, with my experience, has been mostly true) is that they constantly whine about being depressed, as if looking for sympathy, many people, things, etc. that follow that behavior are labeled 'emo' as a form of mocking.