Round here, controlled a/d's are all in class C, and I do seem to remember that this means ALL traffic is controlled and hence separated.
My home base is EHRD, which is class C. Yes, it is controlled in the sense that we need clearance for everything we want to do. That also means that ATC will inform us of the landing order once we get in the circuit. But once we've gotten our assigned number it's up to us to maintain proper separation so that number 2 lands when number 1 just vacates the runway. Ideally, that is. By default, ATC doesn't call you for the base turn or any other turn in the circuit.
Exceptions to this are if you can't see the traffic but ATC can, or if ATC wants to deviate from the 'standard' spacing for some reason: Either putting you very close behind the number 1 because he's a T&G anyway, or further behind because ATC is planning a departure in between.
What also complicates matters is that ATC sometimes uses three different circuit altitudes. If it's busy, aircraft that are doing training circuits are kept at 500', aircraft on the Mike arrival are kept at 1000' and aircraft at Romeo and Hotel arrivals are kept at 1500'. Obviously in that situation it's very hard to see other traffic, so ATC will tell you when to turn base, and when to descend. All in a days work. And great fun once you're used to it.