There are a number of different "ATC" authorities:
Responsible for the movement areas on the physical airport. This includes both aircraft and airport service vehicles. Aircraft refer to this as "Ground".
Gives an aircraft IFR (or sometimes VFR) clearance for flight plans.
Manages arriving and departing aircraft, usually takes over responsibility for aircraft as they approach a runway (take-off clearance) or as they approach the airport (hand-over from approach control).
Manages the airspace around the airport for departing flights providing separation and routing. Sometimes combined with Approach Control.
This is the first authority you talk to that is actually located at the airport. Manages spacing and arrivals and usually assigns runways. Also called "Terminal Control" and may be combined with departure control.
This is the authority you talk to when you are going between airports. Usually a center controls a large area of airspace and can manage aircraft in those areas. Here are a list of FAA Centers, called "Air Route Traffic Control" or ARTCC for short. On the radio pilots usually use the term "Center".
Flight Service Station
This is a service provided to pilots but is not an air traffic control authority. Pilots may open/close flight plans or get en-route weather information on these frequencies. They are usually called "Radio", for example, "Stevens Point Radio, N12345 on 131.2"...
☆ - Typically located on the airport which the pilot is operating. This is not always the case though, there are remote towers and satellite airports that may include these services but not have them co-located with the field.