Classes
Neatly tries to correspond current capabilities of the warship to indicate either frontline service, or secondary duties; second class doesn't mean the warship won't be eligible for the battle fleet, just that it's more dispensable, and might make up the majority of warships.
Ratings
Ratings implies that the technological underpinnings are fairly stable, so that it's fairly easy to categorize warships by obvious capabilities.
Dreadnought
The best and newest (and most expensive) line-of-battle ships are designated dreadnoughts. They form the backbone of the front-line battle squadrons and continually evolve to meet new threats or exploit new ideas. As a dreadnought class loses its cutting-edge status, it is downgraded to Battleship designation. The two hundred thousand tonne Kokirrak class dreadnought is about to suffer this reduction in status, reflecting the fact that the design is becoming obsolescent. Current Imperial dreadnoughts include the Plankwell class (two hundred thousand tonnes) and the awesome Tigress class (semimegatonne), which carries three hundred fighters in addition to its main armament.
Apparently, super would be over a semimegatonne; fast would be with at least a four parsec strategic movement.
Battleship
Including both downrated dreadnought classes and purpose-designed second-class line-of-battle ships, the Battleship designation covers the bulk of Imperial capital ships. Like dreadnoughts, battleships concentrate their firepower in a huge spinal mount and batteries of secondary bay weapons. Defenses include thickly armored hulls and huge sandcaster batteries. Battleships are deployed by preference in massed squadrons, but may be encountered detached as guardships or showing the flag. Battleships are second-class only when compared with dreadnoughts; any battleship is capable of ripping the heart out of a heavy cruiser with a single salvo.
Generally speaking, in internal classifications, second class would be one technological level down from default dreadnought, though if it's modernized, they may retain first class or dreadnought status. Third class would be two technological levels down from default, and generally unmodernized. While there may be a better science fiction term than coastal, it would be am interstellar warship with probably minimum sized capital class spinal mounts, but rather shortlegged, I'd say about factor one or two parsec range in the fifth millenium point of view, considering that factor three is considered the norm. Distant station flagships might require custom built second class battleships, economical operations or specific environmental conditions, rather than deploying an older dreadnought, or one whose performance doesn't make it suitable in the battle squadrons.
Battlecruiser
More lightly protected than a battleship, though mounting the same armament, the battlecruiser is designed for a slightly different role than the line-of-battle. Battlecruisers cannot stand up to their own armament for long, but they are not intended to. Instead, they undertake fast strike operations against enemy shipping or bases, or chase down enemy cruisers doing so against their own side. Battlecruisers sometimes possess a higher jump capability than battleships or dreadnoughts, to give enhanced strategic mobility. The Imperial Navy does not favor battlecruisers, although some of its potential opponents consider them useful enough to deploy in large numbers.
Apparently, your parsecage may vary; it's always been an interesting question how you spell it, battlecruiser or battle cruiser, and that tends to imply how you actually plan to use them, not necessarily stated role(s). Dreadnought armoured cruisers are the technological level twelve expression of this type of warship, and by technological level fourteen, fast battleships, or armoured battlecruisers is the confluence in the requirement of more protection and the minimal compromise of tactical speed and strategic range. A battlecruiser is a capital ship, while a battle cruiser is a very souped up version of an armoured cruiser, whose armament approaches or equals that of a battleship, but isn't expected to be in the line of battle. Light (battle) cruiser, or large light cruisers, are abominations, trying to skirt bureaucratic restrictions and frankenstein a monitor/coastal battleship/battlecruiser hybrid.
Battle Rider
Battle riders are designed to be an alternative to Jump-capable warships. Since a whole squadron can be carried by a huge Battle Tender, the battle rider need not devote space to Jump engines or fuel. The space thus saved can be used for weaponry and armor, while the money saved pays for the lightly-defended tender. A battle rider is up to fifty percent more effective in combat than an equivalent jump-four-capable ship, but lacks the mobility to break off if the fight goes against it. Tenders are vulnerable to enemy action and since their loss will leave the squadron stranded, resources must be diverted to protecting them. The result is that battle rider squadrons are not always as effective as they might at first seem. The concept is not currently in favor with the Imperial Navy, though many squadrons still exist. Some battle riders have been transferred to the colonial fleets, assigned as guardships at depots and strategic worlds, or sold to friendly powers.
That's because their doctrine is probably flawed, not that I actually care; battle riders are supposed to be jumpless coastal battleships, and therefore can operate in deep space.
Monitor
Monitors are large system defense craft intended to take on and destroy incoming heavy units. While in theory they can be equal in capability to a battle rider (indeed, a battle rider can serve as a monitor if no tender is available), they tend to be constructed more cheaply and to lower specifications. Monitors thus tend to have relatively low acceleration – two gee is common – as they rarely move far from the world or installation they are defending and operate on interior lines. Defenses are particularly heavy, as the main purpose of a monitor is to remain “in being” to threaten an attacking force. Actually destroying enemy forces is a bonus, but preventing a landing or bombardment is enough. Some monitors are constructed from hollowed-out planetoids. Such vessels tend to have very low acceleration but are extremely hard to kill. They also have stealth and surprise advantages. The Imperial Navy does not build planetoid monitors but many individual worlds do. The Navy primarily uses monitors to defend its bases and depots. Most naval bases have a force ranging from a single light monitor of about five thousand tonnes displacement to several squadrons of battleship-sized units to back up the more numerous light system defense boats. Although battle riders can just as easily be used, monitors have the advantage that they cannot be ‘poached’ for fleet operations, thus leaving a depot inadequately guarded. The largest monitors are designated Battle Monitors. Although smaller than a typical battleship, they do not give up space to fuel tanks and are thus comparable in combat capability. Heavy monitors are generally equivalent in combat to a heavy cruiser, though they are much smaller. The term Light Monitor is assigned to any sublight combat vessel larger than a gunboat (id est anything of one thousand tonnes and up) but not capable of taking on a light cruiser. Specialist monitors are sometimes fielded, such as missile monitors as support platforms, patrol monitors that carry fighters and small craft to police the outsystem, and strike monitors with heavy armament and powerful engines for a rapid attack on an intruder.
And of course, we come to the crux of the matter: monitors are actually riverine and littoral craft, which means they're meant to stick close to planets, which means that you can design these ships with limited range manoeuvre drives.