I think it all comes down to the tight pants.
I've been punk & metal for who knows how long (21 years at least if you start counting when i got my 18" hair cut into a mohawk at age 12). I listen to metal music most of the time but I identify more with punks, most metal guys are just into beer and women and don't give two hoots about much else. Punks I grew up with we all educated ourselves on racism, sexism, homophobia, government, and all the stuff that makes us "evil" cos we fight/speak against it. We didn't believe our school was any good especially since these kinds of ideas were being propagated by the people in and attending our school. We read our own book selections, wrote/printed our own mags, did a lot of political activity, even though we were in a small town we made a little scene with us and the neighboring towns punks/motivated metallers. The anarcho-punks in Minneapolis called us the "Country Punks: leaping corn fields in a single bound" when we went to AYF meetings and all that to chide us for living out here. But in the end I'm the only hold out who never left the small town but still hold my crazy rather relativist views.
MN had a large goth/darkwave scene especially "back in the day" before Hot Topics made mall-goth popular. The classics were bands like: Alien Sex Fiend, Bauhaus, Christian Death, Current 93, Death in June and London After Midnight among others. Original Goths were basically rich kid punks who got into heroin and black magic/occult topics - usually in a rather silly and insincere fashion with no real knowledge of magical theory and practice. Also, since many goths are rich kids (they can afford the "H") they usually hold aristocratic & republican views quite at odds with the punk scene.
Emos are basically as stated, just emotional car crashes. Cases self-extracted from the above scenes, often by excessive use of "X" and bound for the psyche ward until their Seratonin levels even out. Emo's listen to basically the same music as the other two with an emphasis on the more depressive bands.
But these are my experiences with the old guards of the scene, I can't make any statement about what the Hot Topic punks, goths & emos of today are like. They always look at me like I'm a Narc or a Pedophile when I go in there to buy a classic metal tee shirt... and I'm neither I'm just an old fart punk!