So now you have 12 ships, like the Enterprise and a number of ships not like the Enterprise, yet still sporting a similar configuration.
This is exactly why both Starship
-class and Constitution
-class both work in regards to the Enterprise.
They started with the twelve Starship
-class vessels in the late-2230's/early-2240's. But as they built more and new technology was integrated, they began using sub-class names to describe the differences between vessels.
The Enterprise starts her life as a Starship
-class vessel and at some point is upgraded to Constitution
-class specifications. Either Pike or Kirk kept the original dedication plaque as a reminder of where the ship came from.
EDIT: We have to gloss over the fact that the Enterprise didn't have a visible dedication plaque in "The Cage".