...Of course, if in the real world two outwardly similar ships had powerplants as different as those of the E-refit and the E-A, they'd probably be considered wholly separate classes. Such things have happened in practice on two recent historical junctures: between the world wars, when old coal-firing battleships were refitted for oil powerplants, and during the cold war, when the USN built two lineages of near-identical carriers, one with oil boilers and another with pressure-water nuclear reactors.
I rather like to think in these terms of overarching if complex logic:
1) All Starfleet ship classes are named either after the first ship commissioned, or the first ship recommissioned to a refitted standard.
2) Kirk's ship was originally part of Constitution class, as she was built to the specs pioneered by USS Constitution.
3) Kirk's ship became the first and possibly only member of the Enterprise class when radically refitted for TMP.
4) A bit later, USS Constitution was refitted to a different standard which featured a less-modified shuttlebay and a more extensively modified main powerplant that looked a lot like the later Galaxy class one... This class became known as the Constitution(II) class for a while, until the last original Constitution was kicked out of active service, at which point the refit reverted to plain simple Constitution class designation.
5) The E-A ends up representing the new Constitution specs, either through refitting and renaming, or then newbuilding (and possible renaming).
6) By the 24th century, all this becomes a bit fuzzy, and people speak generically about the Constitution class. Still, Picard is formally perfectly correct when calling the "Relics" bridge simulation as representative of the "old Constitution class"...
Timo Saloniemi