Terminologically, the word 'frigate' appears in four centuries of naval history, and seldom means the same thing twice.
Fleets evolve as technology evolves, names sometimes stay the same and get behind the times, sometimes change their meaning entirely. 'Dreadnought' was a historical accident; it's been an RN battleship name since the 1650s if not earlier. The name simply happened to attach itself to the first of a new breed, possibly deliberately given 'Jackie' Fisher's sense of melodrama.
To try and reach some kind of sensible medium, let's look at what they're designed to do. Battleship, historically a contraction of 'line-of-battleship', basically denotes a vessel designed to project maximum possible killing power, and built to if possible survive the enemy doing the same to it. Speed would be nice, but you can't have everything. Technically, the dreadnoughts were never acknowledged as a separate type, all were given BS designations, assigned to Battle Squadrons, etc.
Cruisers are designed to cruise. They have to be smaller than battleships, because for one thing they aren't built on a budget of 'whatever it takes'. They cover area, blockade and interdict civilian traffic, and act as the eyes and outriders of the fleet. They tend to be serious warships, big enough to be allowed out on their own.
Destroyers began as the fleet's close escort, and rapidly evolved into their main threat. They are small enough to be numerous, fast and agile enough to survive a clash with a much larger ship if not necessarily win, pack hunters and defence against same. The White Star is actually an absolutely classic fleet destroyer type, fits the bill perfectly in terms of function and relative qualities.
The wooden frigate turned into the ironclad cruiser; WW2 and after frigates happened to be about the same size, which is why they inherited the name. Latterday frigates are defensive, and usually against special threats at that. No submarines in space, unless your hyperdrive has developed a really bizarre malfunction.
The Nova is a old, outdated battleship, tactically, and the Omega is a new heavy cruiser, made more effective than it's predecessor by advancing technology.