I think that your assumption is correct,
CuttingEdge100, and that the definition changed/grew as the various series came out. Searching through the TOS (& TAS) transcripts, I believe that "subspace" is
only ever mentioned there in conjunction with radio. Depending on how you define "first," the first mention seems to be either:
"Mudd's Women" (first in production order: episode 4, aired Oct 13, 1966):
Kirk: "They're married. Subspace radio marriage."
or "Charlie X" (first in airdate order: episode 8, aired Sep 15, 1966):
Charlie: "You don't need all that subspace chatter."
later, Uhura: "Captain Kirk, my instruments show we're receiving a message on subspace frequency three, ship-to-ship."
This (exclusively) radio tie-in matches up with the description given on page 23 of the April 17, 1967 version of
The Star Trek Guide: