I’ve been debating whether to add my own personal list, so here it is.

This includes some designations that exist in non-Trek series.
Battleships:
Dedicated warships, bridging a gap between carriers or other large specialty warships and larger cruisers. Battleships are intended to act as an anchor in combat for smaller ships, and a battlecruiser has more emphasis on speed than raw firepower. Generally a bit less powerful than a dreadnought.
Carriers:
Used for deploying large numbers of small craft, be those shuttles for colonization or fighters in a military capacity. Since many of the non-Trek series include fighter complements on other classes besides dedicated carriers, it would seem the latter are somewhat more rare because their main advantage is in numbers, which in turn means less space for the weaponry or equipment that a cruiser or other class could carry.
Corvettes:
Smaller than a destroyer, I mainly see these as light support vessels that can assist larger ships, patrol, and help control smaller local areas. I tend to include ships that might be called gunboats in this classification.
Cruisers:
Pretty much the jack of all trades model, cruisers can handle a variety of missions. Variants include:
Command cruisers: A fairly specialized variant to act as a flagship or sector command vessel, with enhanced communications and systems for coordinating larger formations.
Heavy cruisers: more weaponry for military missions, or equipment for exploration. Suitable to be a core design that can handle almost any mission profile.
Light cruisers: typically a bit faster than a heavy cruiser, with longer range. Perhaps less overall firepower in a battle, but could be useful as a support vessel.
Surveillance cruisers: A type mainly seen in the Battletech universe, such vessels are sort of hybrids between a cruiser and a scout. They can perform reconnaissance or scouting missions in cases where a smaller vessel might be unsuitable, with the flexibility that a cruiser hull can offer.
Destroyers:
Mainly lighter, faster escort and support vessels. Typically not as well armed as a cruiser or frigate individually, but easier to build in numbers. Heavier models would have more firepower and shields, while light or fast destroyers would have an emphasis on speed and range.
Dreadnoughts:
A heavy warship designed specifically for military use, and which can be used as a force multiplier or deterrent vessel. I generally assume that, in a “big fleet” model where a cruiser, frigate or destroyer build might run into fairly large blocks (50-100 vessels), a dreadnought build of around 10-20 vessels in a class wouldn’t necessarily be unreasonable. It would depend on the context and economic base.
Escorts:
Sort of an “in between” role between a corvette and a destroyer, with heavier weapons than a corvette and more flexibility. Variants of a destroyer or frigate can be utilized.
Frigates:
It’s been my experience that the frigate class seems to vary a lot depending on when the series was produced; older books like FASA’s Trek works and Jackill’s tend to view the role as sort of a hybrid between a cruiser and a destroyer. The frigate tends to have a destroyer’s speed and a cruiser’s flexibility. Other works, especially more recent ones, tend to treat frigates as being lighter support vessels somewhat more like my corvette description.
For my part, I tend to lean more towards the first definition, but as with cruisers I think there’s a wide range of options.
Medical ships:
For my head canon, these are typically cruiser or frigate variants designed specifically for medical rescue and transport. These hulls have the ideal range of modularity, speed, and if necessary defense to fill the profile.
Scouts:
Ships designed mainly for range and speed, with typically limited armaments and not for military service (a destroyer can often fill such a role in the military). This would include dedicated science platforms like the Nova and the Oberth.
Strike vessels:
Typically cruiser and frigate variants, a strike vessel has an emphasis on tactical operations but also has potential for exploratory or other missions, being a flexible platform.
Transports:
Generally non-military vessels for traditional missions, including variants specialized as tugs. Some military variants exist, like the troop cruiser (another type more common in Battletech).
Small craft:
In terms of fighter analogs, I tend to view these as mainly being patrol craft and as anti-fighter screens for larger vessels. Interceptors are generally faster and less armored while a bomber can be used for surgical strikes against priority targets.