Actually, I think "Starship class" was consistently used in TOS, not "Enterprise class".
It appears on the Enterprise
bridge dedication plaque and on the Jefferies drawings used in "Elaan of Troyus", as well as in dialogue every time a ship that looks like the Enterprise
is shown on screen ("Doomsday Machine", "Ultimate Computer", etc.).
I was under the impression that "Enterprise class" only appears once in The Making of Star Trek
, right under a sentence where Starship class is also used, and then in ST:TMP.
"Starship class" was canon during TOS, and "Constitution class" didn't come about until the mid-1970's among fans when Franz Joseph's Blueprints
came out the same year Greg Jein's "Jonathan Doe Starship" essay was published.
But I don't have a first edition (I mean the fan-produced mimeographed edition, not the later Ballantine edition) of Bjo Trimble's Concordance
and so I might be wrong about the timetable for the "Constitution class".