There is much confusion between the sub-cultures, so here I will try to explain everything.
Gothic fashion and Gothic culture originated from Bands like Black Sabbath but developed into bands like Candlemass and Within Temptation. The gothic fashion draws heavily on Victorian fashion and Gothic medieval themes.
Gothic fashion consists of leather jackets, chains, black clothing, long hair, steel boots, eyeliner, Victorian dresses, etc.
Although Black Sabbath is a classic metal/heavy metal band, their style and genre can be considered "Gothic;" initially, there were associated with heavy metal.
Later on they developed their sound and fashion to lean towards more Gothic, or associate with the Doom metal genre, though they still weren't considered a Gothic band.
But it should not be confused with "Metalheads", because metalheads are a separate sub-culture related to Goths, but entirely different.
Doom metal and Gothic metal/rock are what is considered Gothic: lyrics deal with morbid, occult, graveyards, death and in general Gothic stuff.
Goths listen to bands like Cradle of filth, Morbid Angel, Black Sabbath, Candlemass, Within Temptation, Marilyn Manson, Dimmu Borgir, etc.
Emo is actually a modernized form of hardcore punk with a emotional style and screaming, Emo bands emerged in the early 90s, with emotional lyrics and melodic song structure.
Emo grew out of the roots of Post-hardcore and emo-punk bands, and it then became associated with the metalcore scene in america in the 2000s,
Emo refers to post-hardcore to metalcore to core bands in general. Emo fashion is distinguished by skinny jeans, wavy hair and band T-s,
Emos listen to bands like Bring Me the Horizon, Slipknot, My Chemical Romance, Black Veil Brides, Paramore, Avenged Sevenfold, etc.
Scene is similar to Emo fashion and music; it's basically just Emo with a mainstream appeal. Scene bands range from nu metal metalcore to deathcore bands.
Scene fashion is basically Skinny jeans, baseball caps, and hoodies. It's like a Emo and Gangster mixed together.
Scene kids listen to bands like Suicide Silence, Attack Attack, Killswitch Engage, Slipknot, Fall Out Boy, Motionless in White, Pierce the Veil, etc.
Metalheads originate from heavy metal and biker fashion in general.
Metalhead fashion includes biker leather jackets, jeans, bullet belts, etc.
The subculture and fashion is similar to Gothic subculture:
Metalheads listen to bands like Slayer, Nile, Death, Judas Priest, Iron Maiden, etc.