For me, a city villa is a house with two full stories without knee walls and a relatively flat pyramid roof.
That makes you exactly part of the majority that markets follow.
I see it the same way as Alex85, although I want to emphasize that the term was introduced from the seller’s side.
The houses that are geometrically similar to today's so-called city villas, which mainly appeared all over Germany in the 1930s, I generally only knew as "single- or two-family houses." At most, someone sometimes called it a coffee grinder. The flat pyramid roofs didn’t exist back then; widespread were hip roofs and mansard roofs.
Of course, there were villas too, which were called manor houses (in the countryside) or villas, industrialist villas (in urban areas). Really villas or palazzos in my opinion only south of the Alps. Castles are older and practically do not occur in the bourgeois building tradition IMHO (exceptions prove the rule).
We were then looking for a house with two full stories and no sloping walls. The sellers always answered, "So a city villa." Fine by me ... In the building permit, however, it says "single-family house."
By the way, the footprint of our house is square. We like it, and a free architectural design was not possible anyway due to the property developer constellation.