I'd still love even comparitive layout of what duties are traditionally assigned to what type of ship in various navies.
So much seems to be unwritten institutional knowledge.
It's all nation specific, even if most of the terms are evolved from the original European terminology. It doesn't help that most of those terms came about before there was any idea of standardisation, let alone unification.
I won't bother going into Carriers or Amphibious Assault Vessels as these are largely self explanatory, but essentially:
A Cruiser is a large to very large surface combatant with a focus on ASuW and AAW (they are capable enough to fill both roles simultaneously) and tactical control of other vessels. They may have some ASW self protection ability, but it won't be much. Cruisers technically should be the control ship for a squadron, to coordinate the actions of the other members of the squadron. In the modern world a Cruiser is frequently interchangeable with a large Destroyer.
A Destroyer is a large surface combatant with a major focus on AAW since the Cold War, prior to that they had ASuW focus although some were ASW focused. Destroyers were the screen units in formations during WW II, where they would present the wall of steel around the most important vessels and actively detach to seek out localised hostile vessels. Once again ASW capabilities should be self protective in nature.
A Frigate is a medium to large surface combatant with a focus on ASuW, secondary role of ASW, with self protection capability for AAW. Frigates have become multi-role in recent years, far more so than any other type of ship. Slightly smaller than Destroyers they are now less about overt combat and more about controlling sea space, but can be capable combatants in their own right.
A Corvette (Not used very often anymore, most vessels in this class are considered OPV or Frigates) is a small to medium vessel primarily focused on ASuW, but occasionally used for ASW. These are small cheap vessels designed to operate relatively close to land and counter the military sea space control. They are not designed for prolonged engagements, intended to skulk about, hit the opponents with lots of missiles, and run away bravely, preventing an opponent from acting in a cohesive manner.
An Offshore Patrol Vessel is a small vessel with a focus on constabulary operations but retaining several functions of high end warfighting, likely to be fitted with missiles and limited command and control functions, they can act as a small Corvette in a very limited manner.
A Patrol Craft is a small to medium vessel with a focus on constabulary operations such as border protection, anti-smuggling and counter-piracy. There is little to no genuine warfighting capability onboard, with no missiles of command and control systems, although they will contribute to surveillance operations.
Cruisers, Destroyers and Frigates are all designed to spend extended time at sea in deep water, they have capabilities that allow them to work together to provide greater effect over all than each of them working separately. OPV and Patrol Craft are minor vessels that will only ever go into combat circumstances in extremis, don't have the fuel bunkerage, food or ammunition for sustained periods at sea, and mostly cannot resupply at sea. Corvettes are a bit of an enigma, which is why there are very few of them around now, they can fill a Frigate's role to a limited extent, have longer legs than a OPV or Patrol Craft, but can't generate a command and control environment like a Cruiser, Destroyer or Frigate, as well as being far more limited in armament.
