(OT) lathes & mills : vocabulary questions

The recent thread about lathes and related machinery leaves me at a loss
with the terminology, me not being a native English speaker.

A) I think I can imagine a lathe, if I understand correctly it is called
a "tour" in French and a "draaibank" in my native Dutch. That means,
the piece of stock you are going to work on is clamped between two
centerpoints, the machine makes it turn, then you press a tool somewhere
and it cuts a circular groove. Right so far?

B) If correct on A, how to understand the dimensions? Perhaps a 36x9"
lathe has 36" between centers, and 9" is the max. diameter of basic stock?

C) if we're done about the lathe, what is a mill (in this context)?
Google wasn't too helpful on this one, given windmills and what not.

Excuse my lack of English profiency, thanks in advance!