As I said, there are differences between Goth and Emo despite the overlap whether in music or fashion. The biggest salient differences for me’s that Goth’s the older subculture with a profound interest in the supernatural/macabre and significantly more sexualised fashions. Emo, to me, hasn’t gone this far thematically and sartorially speaking.
Likewise there are differences between Goth and heavy metal, the biggest one’s that Goth often tends to look to 19th century literature and fashion for inspiration. As far as I know about it so to speak. If Emo and Goth are considered to be punk, it may be parsimonious to say that Emo seems generally less sexualised (not too many Emos wear corsets, let alone as often as Goth do).
Goth seems more like 70s Punk in the sense of wearing openly sexualised outfits (the BDSM influence) and being as influenced by glam as it is by electronic music. Actually and oddly enough, the New Romantic subculture also had a lot of electronic acts and also looked to Bowie for inspiration. (Honestly, punk owes much to glam rock in terms of aesthetic and admitted musical influence or in Paul Simonon’s case, doubling for Bowie.)
If Emo’s considered to be similar to Goth, it’s what Goth would be like if it weren’t for the coincidental or accidental New Romantics confluence (although New Romantics initially didn’t have much to do with Goth, since it didn’t last long it’s likely some of those NR members went on to join Goth). This might be my opinion but it does make sense in a way that both Goth and New Romantic descend directly from post-punk.
Emo’s influenced by post-punk (MCR did encounter Bauhaus and were also influenced by the Cure) but not to the same extent of being in contact with another post-punk scene in its inception. Though some emo musicians may come to do electronic music and some admit to being influenced by new wave, Goth in the 80s was practically contemporaneous with New Romantic.
(This may not always be the case but if NR didn’t last long, some of those NRs would’ve become Goths immediately.)
Also the real one’s that Emo seemed fairly mainstream in recent memory whereas Goth’s generally more of an underground thing. Not that there aren’t underground emo bands and mainstream Goth acts. But I often get the impression of Goth aesthetics and sometimes the Goth sensibility to be too extreme for mainstream press to enjoy that it patronises the likes of Nine Inch Nails and emo instead.
In short, emo and Goth are different enough to have their own sensibilities but if emo’s considered to like Goth it’s what Goth would be like if you remove the New Romantics confluence and tone down the aesthetics significantly. I don’t mean it in a bad way but I do get the impression of emo bands being at some point more palatable to mainstream press than Goth bands are.
So there’s that.