Well, there's how Star Trek has occasionally established "classes" and then there's how real navies establish "classes." The two aren't really the same thing, are they?Would it work to say that the original Ambassador was built to the specs of the Enterprise-C. The majority of production run Ambassadors, including the Ent-C, were built to these same specifications. The Ambassador herself was then seriously damaged in some-action-or-other while serving as the starfleet flagship causing her to be majorly refit to the Probert design. While her then prestigious role made her worthy of a refit the much-speculated problem with the original spec made it the remainder of the fleet unworth, unsuitable would perhaps be a better phrase, of the same: hence the later Ambassadors we've seen haviong Ent-C specifications.
But that's being needlessly convoluted. Why not just say that they're two different classes?
In real navies, the purpose for establishing a "class" is for planning purposes. Any two ships of the same class are, in every meaningful way, interchangeable. They have the same capabilities, and require the same servicing and support mechanisms.
This doesn't necessarily mean that two hulls from the same class are identical. If the same ship class is manufactured in two different dockyards, it's actually quite common for there to be differences... sometimes SIGNIFICANT ones... in the physical configuration.
In Trek, of course, the "classes" idea always worked very well... until ST-VI redefined the refit design as being "Constitution class." Prior to that point, it was defined... PROPERLY... as being a class named after the first ship in that configuration. That being, of course, the Enterprise. They even mention the "Enterprise Class" on the outside of the ST-II "Bridge simulator" module where the Kobayashi Maru is taken.
Personally, I treat the print in ST-VI which referred to the 1701-A as "Constitution-class" as being a production error, on the same level as the "78-deck primary hull" seen in ST-V.
The first ship of a given configuration is always the "class ship." Change the abilities or performance of a ship of that physical configuration in any signficant way, and the ship is no longer "interchangeable" with the earlier ships... hence it becomes a new class.
So... if we treat Probert's Ambassador and Sternbach-et-al's Ambassador as being able to be serviced by the same facilities, and having the same capabilities... ie, of being entirely interchangeable from a logistical and operational standard... I have no problem envisioning one as being built at Utopia Planitia and one being built at Starfleet Division, San Francisco. (Just for example)