RL carriers are cheaper and faster to buold for their tech level than battleships. Not sure what the difference would be like in space.RL frigates, for the most part, exist to carry specialised gear and, as escorts, ger in the way and take hits so capital ships (much harder to repair and replace) don't. Not that that part really works anymore with the changes in weapons systems. Desrroyers started out explicitly as 'torpedo boat destroyers', another small, specialist role ship, they were built to prevent the even smaller and cheaper torpedo boats (and later submarines) from sinking the capital ships, which couldn't defend against them well, again, in the last, by taking the hit for them if they had to. for whatever reason these were built up to have more of a direct combat capability over time, but they're still on the 'pointlessly small and squishy' end so far as direct fleet combatants go... if... direct fleet combat was still a thing. Not sure how Either of these translate into space born operations beyond probably being less efficient in terms of 'stuff that makes the ship work' to 'ability to kill the enemy', and whatever that does to cost.
Cruisers, IRL, are devided up differntly by different navies, but ultimately are designed to opperate solo or in small groups against just about anything, doing just about any job compitently (with the obvious exception that they're quite blatantly not carriers.) They also tend to make up the bulk of the standard firepower in any fleet designed for direct combat. Translated into space... they would fill pretty much the same job slot by definition.
Battleships, by simple virtue of their size and thus massive amount of structural redundancy, are built to out range anything else, hit harder than anything else, take more hits than anything else, and flat out not sink until everything else on both sides is Dead. That same size does give them some vulnerabilities though. Even with proper countermeasures, torpedoes are still a problem, and for all that Sinking them is an insanely difficult task, disabling and crippling them is well within the capabilities of enemy bombers. They make Excelent commabd and control platforms by way of their durability, and provide pretty much the Best heavy artillery support any costal opperation could want. The only bigger guns are fixed emplacements, or the sillyness that was the german Railway gun (the origionals of which were a ww1 stopgap to allow already existant naval guns to be used as land based artillery). The main reason these things don't go into combat solo is how insanely expensive they are to produce. In space? Well, depends on the design philosophy, but they're basically bigger, bashier, tougher, but somewhat less agile crusiers, with bigger and/or better everything.
Dreadnoughts: IRL, this was simply a change in philosophy for the design of the battleship, and the introduction of new construction techniques. Rather than having a tone of different types of guns crammed in everywhere they'd fit, it just had as many of the biggest ones as it could practically mount, then what amounted to point defence weapons, and maybe some torpedoes. Probably made it more dependant on it's escourts, but superior in every other way. In sci-fi, it's usually treated as being to a battleship what a battleship is to a cruiser, which is odd.
Carriers: IRL, these take advantage of the capabilities of aircraft to allow stand off engagements from outside of detection range of enemy fleets. They're cheaper and a hell of a lot squishier than battleships, still need a full escourt fleet... and the vast majority of the time they'll rip a battleship based fleet to shreads for the same reason horse archers shreaded mideeval and earlier armies: they use superior range and manouverability to flat out refuse to engage you in such a way that you can hit back. If you have your own carrier, the result is a lot of destroyed planes... and decent odds of both sides bombers going through anyway. Or neither. It depends what the commabders do with them. A fencer's duel rather than the battleship's slugging match. Finally, it's planes allow for a dramstic increase in how far away it can detect the enemy from.
In space, everyone can opperate in three dimentions, and there's no curvature of the earth to limit detection range, reducing the carrier's advantages dramatically. It's Still easier to kill than a battleship, a drone's weapon's damage output, unlike a plane's bomb, is Not going to match the damage output of a cruiser or battleship's main gun, and various other similar things that I'm no longer coherant enough to articulate right now. It still has the nice advantage that it (hopefully) doesn't get in the fight itself and drones are a lot easier to replace than ships, drones probably Can still deal with small ships, and depending on the design make great ecm platforms. Whether they actually help detection range compaired to just having bigger, better, more powerful sensors is debateable.
I had a point when i started this. It's now just a giant info dump. Typed up on a tablet in SV's quick reply box.