Prepare to enter into my murkiness...
Do programs define these fields of study precisely, or according to the hermeneutics of their own departments? Judging from my research, it seems that how the departments define their own programs can greatly affect a candidate's research trajectory once they enter.
I think that what historical theology means is that basically one studies theology concurrent with the histories surrounding those theological developments. The difference between programs seems to be in the emphasis upon the "theology" part or the "historical" part. No?
So what, then, would the difference be between "historical theology" and "history of Christianity"? Seems like a change in terms means some sort of shift in emphasis, but that is unclear.
History of religions, on the other hand, would seem to emphasize the historical dimension and decline to make a judgment upon the theological dimension or the question of truth because of their treating many religions in the same department.
Please, someone with the γνωσις, educate me. Trying to find clarity from department web sites is challenging.