"Are you willing to help us overpower the Romulan B-type Warbirds we may encounter? Are you prepared to help us detect them through their cloaking shields? You see my problem, Admiral."
- Captain Jean-Luc Picard to Romulan Admiral Alidar Jarok, 2366
Picard later refers to the "Warbird Class starship", presumably the Federation designation of the D'Deridex Class. On this and, as I recall, another occasion on screen (but not this), spacecraft were referred to not just by class, but with an additional letter designator, suggesting subtypes. I don't think we need a huge taxonomic heirarchy here, but the simple fact is that the Enterprise-B, for instance, would thus seem to be a B-Type Excelsior (conveniently). The Enterprise refit and 1701-A would be a B-type (or perhaps C-type or D-type) Constitution.
There's more than just this, though . . . including some surprises.
Picard's use of "B-type Warbird" seems to be similar to the current letter suffixes used to reflect differences among certain aircraft types, such as how the F-15 fighter has minor variants like the F-15A versus the F-15C. In the case of those two, the latter is an upgraded version of the former. However, the F-15B isn't an upgraded F-15A, but instead a two-seater. Then there's also the F-15E, which is a multi-role (fighter/bomber) two-seat aircraft rather than just a fighter, so in principle one could have F-15Cs being built as fighter complements alongside the F-15E multi-role strike aircraft.
In other words, it doesn't necessarily imply advancement and improvement, but can also simply imply difference of other kinds, perhaps permanent.
Numbered Blocks and Flights
The fighter lettered type system works a little differently than the older block designations. With blocks, one would basically always have an (imaginary) F-99, for example, whether it was Block 1 or Block 50. However, with lettered types, the block system can be somewhat graduated. In the case of the US Air Force F-16 Falcon, the block system at first appears to be a mere subset of the lettered types, but in the case of single-seat A and C types, the block numbers never overlap, but instead rise consistently.
Interestingly, the presence of significant upgrades is not the trigger for letter types versus blocks, nor are the types and blocks necessarily in chronological arrangement. The F-16A and B Block 20 came eight years after the F-16C and D, by which point they'd reached Block 50 and 52. The Block 15 F-16A and B featured changes in exterior surfaces, hardpoints, radar . . . a huge change, yet we didn't hit C and D until Block 25.
(The 50 and 52 scheme is a bit of a throwback to the far older US military aircraft designation system which is too convoluted to go into . . . suffice it to say that the old system had a lot to do with the manufacturer, meaning an aircraft -- like the Corsair with its famous oddly-bent wings -- made by more than one manufacturer could end up as the F4U, the F3C, the F2G, and more. In the case of 50/52, it's about the engine manufacturer.)
The US Navy also uses blocks with a Roman numeral, in a manner similar to aircraft lettered types, such as for the new Virginia Class subs, though they also use the term "flight" in a similar manner, as with the Los Angeles Class subs or the Arleigh Burke Class.
Some of these lettered types or numbered blocks and flights could be things to which one could upgrade . . . the F-16V, now renamed the F-16 Viper, is Block 70/72, and certain Block 40 F-16Cs are being upgraded to this standard.
Applying all this to Star Trek starships, we might expect the Hood, NCC-42296, to have been a rather different numbered block or flight at construction than the Repulse, 2544, but, while one could suggest they're a different lettered type, I'd tend not to ... structurally, they're identical.
So, the way I figure it, the Lakota in DS9 was an Excelsior Class, B-type, Block/Flight/Refit (Something). You could use a year, but that might not be good. After all, the Lakota was a tactically uprated Excelsior B-type, whereas there's no reason you couldn't have one optimized more for scientific duties in the same year. That said, since we don't know the "actual" number, or even technically the lettered type (it could be that there was another significant Excelsior mod that appeared before the Enterprise-B, and of course there's no reason Starfleet couldn't have other types to which the Lakota belonged), there's no reason not to say Block 2372.
Finally, I'd tend to use Block over Flight simply because "Flight 1234" sounds too much like a commercial airline trip.
The only small issue is what's always been done for ships of unknown classes . . . the "Valdore-type", for example. Is that confusing against "B-type"? I don't think so.
The Constitution, as I mentioned earlier, could have more than just two types. We should pause here to contemplate what I mean. I base that on the fact that certain older ships like the Constellation 1017 were exclusively represented by an AMT model kit with difference to the usual set of filming models used for the Enterprise, at least in the original effects. We could thus argue that this ship actually is of a fundamentally different (albeit quite similar) series of shapes to the Enterprise 1701, and that this may in fact represent the A-type. Additionally, the original pilot "The Cage" featured exclusively shots of the 33-inch (a.k.a. 3-foot) filming miniature in the few ship exteriors shown at the start and end, save for one shot of the early pilot version of the 11-foot used in the bridge zoom-in sequence. There are some differences in the structural lines of those two models, most notably in the saucer underside where the three-footer's lower saucer decks are a bit fatter (i.e. more convex) than the 11-footer. One is tempted to squeeze in a type just from the 33-inch . . . or else to discard the 33-inch's differences as being those of a prototype model, which it basically was.
However, there's also the little detail of shipboard graphics of the Enterprise which also have that same saucer shape, along with different shapes for the secondary hull and the nacelles. While we could also discard these, there's actually precedent for the Enterprise of one shape having onboard graphics of a prior shape, such as Chekov's security graphics that appeared in Star Trek III, lifted from Franz Joseph's technical manual:
Some would protest, at this point, noting that the Enterprise herself had different models representing her, including another AMT model kit. This is true, but in the case of the Enterprise the very point is that there are multiple models representing the same ship. Yes, one can argue that the Constellation's model was merely an attempt to represent a starship like the Enterprise, and that's true, but there's simply no evidence that the Constellation looks any other way.
Further, it may suprise you that the Ambassador, Galaxy, and even the Sovereign all have multiple possible types. The Enterprise-C has significant structural differences from the Zhukov model, for instance (and I'd kick myself for not sharing with you the awesome DJ Curtis Ambassador which is totally my headcanon C-type Ambassador).
There were also significant structural changes for the Sovereign Class between the films, including alterations of the saucer-secondary dorsal connections and changes to the nacelle and pylon angling and position . . . a not-insignificant refit. Add in that one doesn't just slap on weapons and store antimatter warheads in any old room, and the Nemesis Enterprise-E is quite a different bird than the First Contact ship we saw. Is it enough to be another type? You be the judge. At minimum, such rapid extensive refitting suggests a failed class of vessel, but then I'm not a Sovereign fan anyway.
Then there's the Galaxy . . . but I'll have to save that mess for another occasion.