That doesn't change the fact.
Sure it does: it means starfleet officers (like all humans) do not use strict terminology at all times.
On the other hand, somebody at HQ commissioned a plaque that read "Enterprise Class"...which would only happen with a conversion.
The one phrase you never see on screen is "Constitution Class Refit" which (AFAIK) is some mumbo-jumbo invented for the Encyclopedia, a piece of tie-in merchandise.