This is the Classic Enterprise, and here are my versions of her established plaques, plus one of my own creation.
In our STU, the original Enterprise, completed in 2245, was the very first "starship", a title bestowed upon her by the instigator of the "Starship Program", Captain Robert M. April, who would later be her first captain as well. All other ships beforehand were single-duty vessels referred to by their role, such as cruiser, scout, survey ship, etc. and as such, all the ships from before and around the time of Enterprise's launch were referred to as "cruiser class", "scout class", or some such. With the launch of the Enterprise, the first true multi-role vessel large enough, powerful enough and capable enough to be a multi-role platform, and she and her subsequent eleven sisters were referred to as the "starship class", and as such, this was reflected on her dedication plaque, as above.
With later ships, such as the Bonhomme Richard sub-class (or Constitution class Batch 2) USS Endeavour in 2253 and the Indefatigable sub-class (or Constitution class Batch 3) USS Defiant in 2260, they were referred to by their original class ship blueprint designation of "Constitution" and this was reflected in the later ships' dedication plaques, but the original twelve "starships", since converted into command cruisers, were still special and unique among the roughly ninety other ships of that same nominal class in service by 2265.
As previously stated on my Endeavour page, my opinion as shown above is that, because the Movie-style (or in fanon, "New Technology') refit of Enterprise was a literal re-building of the ship, all such refitted ships got a "re-commissioning" plaque as well. They were, in effect, almost entirely new ships and deserving of plaques of their own. This re-commissioning stardate is mere days after the end of the V'Ger Incident, by Andrew Main's 0.1 stardates-per-day system for the period between 'The Motion Picture' and 'The Wrath of Khan'.