Akai Kenshi
Forgive me for asking a dumb question, but would it be fair to say that goth/death rock is in part characterized by the relatively sparse use of rhythm guitar? I was just listening to Christian Death and thinking about how stripped down it sounded, but then I realized that Bauhaus really doesn't use too much rhythm guitar either. It's mostly just leads, bass and drums.
Generally thats the defining difference between deathrock and horror punk. Deathrock and goth rock mostly use the guitar for effects like feedback or a bit of rythm while the bass is lead. When you think of great deathrock songs like Romeo's Distress (Christian Death) and Evil (.45 Grave) what most people remember aside from the lyrics is the awesome bass riff. Horror Punk bands focus on guitar and vocals, Misfits for example, you remember Danzig's vocals and the guitar riffs, notably on songs like We Are 138, Halloween, Die Die My Darling, Some Kind of Hate, and Last Caress. A more modern example would be Cinema Strange's Greensward Grey (opens with some feedback or a bit of synth and then the bassline carries the song through) and Calabrese's Vampires Don't Exist (liberal use of guitar, powerful vocals).
Deathrock = Bass and Drums
Batcave = Bass and Synth
Horror Punk = Vocals and Guitar
I know Deathrock and Batcave are generally considered the same thing but I notice a difference in general sound between the two, deathrock having a faster tempo with a bit more guitar and batcave having a slower tempo and using synthesized effects, probably because of the rise of New Wave around that time period in Britain.