Genres are subjective and usually opinion based.
there is no "right way" to classify a band but there are certainly wrong ways..
with that said, it seems often that people mix them up.

i generally would classify the mixture of Goth and Punk into 4 main subgenres:

Deathrock- (Christian Death, 45 Grave, Voodoo Church, Kommunity FK)
usually based in CA or directly influenced by one of these bands.
known for prominent bass lines, eerie guitar, and dissonant vocals

Horror Punk- (Misfits, Undead, Mourning Noise, Rosemaries Babies, Michael Graves, etc.)
known for catchy melodies, rockabilly vocals, and horror themed lyrics. usually more musically aggressive than deathrock
Goth Punk- (Damned, Grong Grong, Flower Leperds, The Willard, late 90's AFI)
i would generally say that a band is Goth Punk if they have Goth and Punk influence but don't sound deathrock/horror punk.
Psychobilly- (The Cramps, Deadbolt, The Hangmen, Demented Are Go)
fast tempo goth-rockabilly sound with tongue in cheek lyrics

Goth Rock is Goth Rock, if it doesn't have punk influence it isn't deathrock...
Recently people have been calling it "Darkwave" as an effort to distinguish the genre between
what the ignorant masses have thought to be Goth Rock (nu metal crap)


As music evolves, more genres are bred and many prematurely.. shoegaze, zombiecore, dream pop, etc.
these are all styles of sound that people have named music, not genres.
Douglas Pierce describes his sound as "Apoctalyptic Folk" that doesn't make it a genre its a way of describing your sound..

when Death in June becomes the foundation for a whole music movement (and not just a few bands)
Apoctalyptic Folk will be considered a genre to me..

as for Zombiecore those are just thrash metalers who like the misfits
and Shoegaze is the stupidest genre name ever...