Emo was originally a nickname for "emotive hardcore" (type of music), but has evolved into meaning "emotional" because it was misinterpreted, since fans of this music were ususally known for being a bunch of depressed-self-harming-teens with too much free time. It's all stereotypical. But this is what it's known for now. An emo person (like I said stereotypical) would be very depressed, hate the world, including themselves and probabl cry all the time. They've even stereotyped and emo style. Usually "emo" kids dress in skinny jeans, dark colors (but not all black), band tee shirts, and chucks. But, like I said about 5 or so times. IT'S ALL STEREOTYPICAL!!! And it did originally mean "emotive hardcore". (and if some one dresses like that it doesn't mean they're gonna go suicidal!)
The word "gothic" was originally used to descibe works of art that were "dark", which is the meaning, hence how it now descibes people we call "goth".
Gothic is now used as an adjective is ususally used to discribe people who wear all, or mostly black. They're usually gloomy. And people think that they do some sort of devil worship. They're sometimes depressed, but everyone can get depressed, so that doesn't really count. Gothic style is: (like I said) all or mostly black, heavy eyeliner, black or odd colored hair. This too can all be stereotypical. Like you can dress "goth" and not worship the devil. You can say you're goth and not worship the devil. There's a goth style music too. It's like a form of rock. Sort of.
But like I said, through this whole thing. Most of this is stereotypical, especially all the "emo" stuff. It's kinda sad how things can get so stupidly out of hand.
I didn't write this, I got it from here:
link
Hope it helps you :)