wait, reading your replies - does city sometimes mean something different in the US? Like, does it not refer to the equivalent of NYC, Paris, Jhb?

Re: city vs. town etc. To steal a phrase from Judy G. Russell, who blogs as The Legal Genealogist: "It depends." If you are doing local history / family history research, the answer depends on the laws of the state / commonwealth you are doing research in.

Colloquially, yes. Legally, It's Complicated (tm).