Do a search for "Yellowstone", and you get other threads where your questions have been addressed.
That said, I stayed in Tetons, and drove into Yellowstone one day. Very heavy traffic, so that took lots of time. While camping in Tetons (Coulter Bay, or others on the north end) is very nice, if you intend to spend most of your time in Yellowstone, it will take much more driving.
But, Teton National Park has lots to offer, also. Depends on what you are looking for. We decided that there was too much traffic in Yellowstone to warrant another trip in on another day, so we did not see much of that Park.
Happy travels!