The FCC is the ultimate authority on radio frequency usage in the US. 47 CFR § 87.5 has the definitions of the aviation services.
Aviation support station. An aeronautical station used to coordinate aviation services with aircraft and to communicate with
aircraft engaged in unique or specialized activities. (See subpart K)
Subpark K:
§ 87.319 Scope of service.
Aviation support stations are used for the following types of
operations:
(a) Pilot training;
(b) Coordination of soaring activities between gliders, tow aircraft
and land stations;
(c) Coordination of activities between free balloons or
lighter-than-air aircraft and ground stations;
(d) Coordination between aircraft and aviation service organizations
located on an airport concerning the safe and efficient
portal-to-portal transit of the aircraft, such as the types of fuel
and ground services available; and
(e) Promotion of safety of life and property.
Domestic VHF use is described in § 87.263. In general, these frequencies are used for communicating with aircraft, or between ground stations. There are various restrictions on certain frequencies/ranges, and despite the name, some are allowed for use on international routes.
Back to § 87.5:
Flight test aircraft station. An aircraft station used in the testing
of aircraft or their major components.
Flight test land station. An aeronautical station used in the testing
of aircraft or their major components.
Flight Inspection is not defined in § 87.5, so it may be the FAA setting these aside for their own use, but these frequencies are used by the FAA for ensuring "the integrity of instrument approaches and airway procedures."