The big round adapter that came with my 2004 Escalade appears to have 4 connectors and the receiver has 6 connectors and a center one for a total of 7. My son has a big round adapter that he uses with his Jeep (it is the same size and will fit in my receiver), but his has all 7 spaces with connectors?

Are they interchangable? When do you need the 4 and when do you need the 7?

The 7 pin is for multi-Axle trailers with brakes.
Most trailer plugs are unique to the make of the vehicle. You should have an adaptor in the vehicle for 4 pin (Standard) trailer harness.

If you use a trailer with brakes make sure it has the male plug on it's wiring that will fit the receiver on your 'Lade. The brakes require a separate circuit and you will need to install a brake controller under the dash. The other connections are for back-up lights & aux power. If you are going to pull a trailer without brakes it's wiring should have the 4 pin plug that fits the adapter that you described.