According to what some other people on here have posted
FCC's Part 95 definition of a base station:
"BASE STATION: A station at a fixed location that communicates directly with mobile stations and other base stations."
In other words, by simplex. If you are using a radio at a fixed location through a repeater, such as with a mobile radio on a power supply on your desk, the FCC considers that a "control station".
"CONTROL STATION: A station at a fixed location that communicates with mobile stations and other control stations through repeater stations, and may also be used to control the operation of repeater stations."
My mobile unit will be a control station at that point.