I think that just a few designations are better. In my opinion the longer names seen in the fandom like "advanced heavy tactical command frigate" might exist in the sense that they explain why two designs/classes of similar size or configuration might coexist, but I cannot see them being used in regular daily parlance.
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A short set of terms like this makes sense for daily use. Here is the version I think about when analyzing the series, modifying the TNG tech manual system.
Explorer (peacetime name for Battleship)-big, expensive, only Galaxy and newer
Cruiser-general use ship, on the big side, covers most hero ships up to Ambassador
I'd also add frigate (may operate with escorts and scout in Destroyer Unit in wartime) - general use ship, smaller than a cruiser, includes smaller hero ships like the Intrepid, OG Connies and similar-sized supporting designs like Mirandas, New Orleans and similar. Mentioned in dialogue, rather than the TM so canon.
Cargo Carrier (peacetime name for Fighter Carrier)- big, but unlike the real Navy, smaller than a cruiser, Akira would be an example.
Tanker-smaller, still capable of general duties, or carrying supplies, like the Ptolemy.
Surveyor/Escort (peacetime name for Destroyer)-small, operates on the edge territory, mapping and some border policing, but can also carry cargo (Antares from TOS)
Scout-small, fast, plentiful, inexpensive, (Grissom would be a newer example)
So that keeps it down to 6 quick designations. But, an Intrepid and a Steamrunner might both be Destroyers with different longer classifications, but I don't like to use them often![]()
While I buy the idea of Surveyours and Escorts being a similar "size", IMO it's more likely that they are a pair of complementary designs intended to work together in fleets (tho they might be able to swap in extremis).
Either Sabers or Defiants would be the Escorts to the Nova's Surveyour.