as an emo, not all emos are metalheads too. they are two completely different genres
for example emo stands for emotive hardcore which is derived from the hardcore punk scenes of the 80s + 90s. while both genres have screaming, they are very different. emo is honestly more close to grunge than metal.
that doesn't mean that emos can't be metalheads as well as the other way around too.
I think the calling metalheads emo thing was just kind of preppy people seeing the dark band t-shirts and clothing same as most other alt subgenres and thought they're the same thing so they just kinda call all of it "emo" or "goth" because they don't know any other terms for it
