One of the difficulties in creating science fiction worlds is creating a naval setting. Starships are incredibly critical in most science fiction settings, basically replacing trains, ships, and airplanes all in one go.
In most cases, I'll have some idea of how the universe works - a specific set of technologies, a specific kind of culture, that sort of thing. But when I was a bit younger, I had a really hard time putting things into a reasonable military (or pseudo-military) structure. This is because whenever anyone talks about navies, they talk in exceedingly specific terms and concrete examples. I needed general information, and they were drowning me in trivia.
It came up again this month, with a new setting I developed, so I figured I'd go ahead and write a bit about the naval terminology and structures I tend to use.
These aren't really based around any real-world navy, but they are feasible enough and flexible enough to form a scaffold. Obviously, if your starships are so rare that they never form into fleets or task forces, this isn't necessary.
First off, I start with a very quick overview of how shipping works. The reason for this is because military vessels will usually have the same spectrum of sizes as shipping vessels. This is for two reasons. The first is because you build the space frame sizes you're comfortable with, and the second is because it's hard to supply ships that are larger than your supply ships.
If your planets are largely self-sufficient, then there won't be any ultra-heavy space trucks. In turn, that means there won't be any death stars. On the other hand, if you need to ship massive quantities of food and metal, you're going to have massive military vessels. The bigger the freight requirement, the bigger the biggest military ship.
Similarly on the small end. "Space fighter" is a pleasant thought to most science fiction authors, but it only makes sense in settings where there are civilian uses for a tiny interstellar ship. Because of this, I tend to only use fighters in settings where there is no FTL radio - the small ships are essentially messengers. Obviously, you can go against this rule if you like, but I find it makes more sense to follow it.
Similarly on the fast versus slow. Do you have "jet liners" for people to travel from star to star, or are they more like "ocean liners", taking weeks or months? Well, the military's gonna have the same kind of preference, taking into account their additional need to keep an active presence in a given theater for months at a time.
With that out of the way, you can begin to think about the kinds of combat encounters that might crop up, and begin to think about the kinds of ships which fit the role. In general, the terms used by real-world navies are pretty adaptable. You might get looked at a bit funny initially, but once it becomes clear that the role is warped by the technology, the players will accept that the real-world name still fits okay.
Now, I can list a bunch of kinds of military operations you might want to have - for example, orbital domination (requires a vehicle that can deploy and control thousands of satellites) or blockade running (requires vehicles that can stealth and vehicles that can detect that). However, the encounters you want in your world will shape the world you build.
Not every setting has blockade running. Not every setting has orbital domination. Not every setting has mines. Or drop-pods. Or interdiction. Or even carriers. It all comes down to the kinds of battles you want to happen in your setting. You can always retroactively add more if you feel the need.
The key is to identify the kinds of scenes you want. Do you picture marines rushing out of a smoking drop pod? Do you picture bombers harassing a burning supercarrier? Do you picture a destroyer floating above a frigate, pulling it in with tractor beams? The vivid imagery you have in mind will immediately tell you the kinds of ships you need.
Then it's just a matter of giving that class of ship a vaguely suitable name. For this, you can read up on military classes like "destroyer" and "battleship" and so on, but remember that those are typically roles not sizes. For example, a "destroyer" isn't defined by its size, but by its role as an anti-submarine escort to larger ships. A "cruiser" isn't "bigger" or "smaller" than a "destroyer" - it's a vehicle that's built to operate for a long time unaccompanied.
By these rules, the Enterprise of Star Trek fame is a cruiser. See?
You could also just invent your own names, of course. Don't know what class the psychic vortex ship is? Just call it "psych-class" or whatever.
Anyway, that's how I do starship design in scifi settings.