Ground will issue taxi instructions. They are also in the tower.

The tower is usually what they call the local controller. Local controllers will issue takeoff and landing clearances.

Departure/approach is sometimes within the tower and sometimes at an entirely different facility. It is also called the TRACON. The TRACON will handle flights up to a certain altitude. Generally it’s somewhere between 10,000 and 15,000 and usually extends to about 50 miles away from the airport depending on the city. They will send you out through a fictitious “gate” and then off to the center. Imagine a squate around every city. Usually four corners will Be arrival gates where the center will put everyone in a line to go through and then approach will take it from there. Likewise, every corner that isn’t an arrival gate is a departure gate where you’ll go out of.

The center will deal with you for every other phase of flight whether you are just overflying or not. Centers are big radar facilities and are spread out. So Atlanta Center will actually handle Atlanta, Birmingham, Charlotte and lots of other smaller airports including lots of GA airports and they’ll work you down to the surface in those cases without an approach/departure controller.