I think your ETA is more or less on target: Latin and Greek have several words for "place of worship", mostly distinguished by function or architecture: templum, aedes, ara, naos, nemus, taurobolion. Only "taurobolion" implies a particular religion or nationality, and that's because the Mithraeans are the only ones to have that particular function, of having a bull's blood pouring over the worshipper.

The Christians invented a new word, kyriake, the Lord's house, because they didn't think they were doing the same sort of thing as other people.

Anybody know Hindi?