Do you have to have separate circuit breakers for a dryer and an oven?

Yes. These will be double breakers. Some 240V breakers have two handles tied together, some have a single handle but are double breakers (take two spaces)

And typically a dryer requires a 30 amp 120/240 volt circuit, while a range requires a 40 amp 120/240 volt circuit. Each circuit uses different size wire.

Why do you ask?

This is already being discussed in your other thread.