The feeder cable for a 30A to 40A subpanel is supposed to have 4 conductors? 2 live, 1 neutral, 1 ground. Correct?

I have a Cutler 200A main panel. What kind of a "feeder breaker" would I use to be able to drive 2 live wires in this cable?
Thanks very much!

The description of the conductors in the cable is correct. What you also need to know is the amperage the cable is to carry. If the distance is over 100 ft. then you should also consider the voltage drop. The total end to end voltage drop cannot exceed 5%.

If you want to carry 30 Amps then you need 10/3 cable.

If you are going to use 40 amps, then you will need to use a #8/3 cable.

I will be going 2 feet at most. So I will use either a 10/3 or an 8/3 cable. What about my second question:
I have a Cutler 200A main panel. What kind of a "feeder breaker" would I use to be able to drive 2 live wires in this cable?

I will be going 2 feet at most. So I will use either a 10/3 or an 8/3 cable. What about my second question:
I have a Cutler 200A main panel. What kind of a "feeder breaker" would I use to be able to drive 2 live wires in this cable?
Either a 2-pole 30A or a 2-pole 40A, depending on which cable you use.
Make sure it matches the panel type. Mainly Cutler has CH and BR style breakers.