I've always assumed it was option 2, because option 1 makes no sense to me. The cosmology of BtVS isn't exactly sensible or internally-consistent or driven by anything other than the needs of the next script, however. Where do souls come from, anyway? Maybe they're recycled all the time normally. But if not, it would be pretty cruel to snag a soul that was somebody else (because the soul is the self, it does not belong to self in this interpretation) and shove it into a vampire as a curse. Then there's the Problem of Dawn.
I always end up having to answer these questions for myself when I write certain kinds of BtVS stories. My answers vary, because exploring different possible answers is part of the fun. Probably the clearest exploration of this I've done was in "The Antique Roman", where Ethan's revenge depends on the explanation of how demons & souls work. And there I assume that the soul that Angel has been cursed with was Liam in life.