THe term Escort Carrier came in WW2 when the Allies built small, slower carriers on merchant ship hulls.  These CVEs were used to escort convoys in the Atlantic and CVEs in the Pacific supported amphibious assults with their aircraft.  The Allies built over a hundred of them...

IMHO, regardless of setting, you generally have three types of ship which roughly correspond to wet-navy roles as follows:

Battleships - dedicated combat vessels, whose sole mission in life is to destroy the other guy's battleships.

Cruisers - multi-role vessels, with enough weapons and defenses to stand up to anything except the other guy's battleships, but not so much of an investment of resources that they can't be risked on exploration, scouting, or diplomatic missions.

Escorts - primarily intended to guard non-combatants from pirates and unforseen dangers. Tend to square off against their opposite number in fleet actions and essentially cancel each other out. Can be indispensible against unconventional threats (torpedo boats, submarines, etc.).

Beowulf is a follower of Jeune École. But we already knew that .  (and no its not an insult look it up)

The issue of classes of ship in the real world are influenced by many factors which starmada does not address, such as operational considerations, politics and resources availability. The CRAT DRAT are a measure of combat effectiveness ans SU is some measurement of size but ships are also impacted by finances.   
Like the recent thread on fleet composition it all depends on the setting. If, as many do, you competitively design and test them in 'gladiatorial' combat then the 'correct' solution is very different from you a playing a campaign and you need a fleet were your dreadnought has to be in many places at the same time.

A follower of Mahan then sorry :? .

A WW1 fleet would not have cruisers in its battle line. Aside for the light cruisers squadrons at Jutland used for scouting the frigates of the sailing era and the attached light cruisers at Jutland were for communications, repeating flag signals from the admiral to their squadron. DN/BB/BC and DDs would have done most of the fighting.

Prompted by your hull sizes Beowulf, I've just done a very rough comparison between German, British, and US WW1 fleets and the displacement of a 'battleship' was about 30 times that of a destroyer. A destroyer of 10/10 should  compare with a DN of 300/300!  Hmmmmm.

I was not suggesting battle ships should be bigger just thinking about comparisons. I once played a great per dreadnought game called Steam and Steel  which had 1 hull space = 1000 tons = 1 destroyer! It worked really well with destroyer flotillas sheltering behind the battle line then charging though to deliver a torpedo salvo.

It does show that a person needs to decide on the 'period' they are 'modeling'. Deploying a flotilla of Arleigh Burkes would be ridicules and having a displacement of 9000+ tons they are quite large at a third of the displacement of a WW1 dreadnought.   

So back to the original question what is a DD?

Former US Navy Gunners-mate here & veteran of the "Cold War" between USA & USSR.
US Navy classification uses abreviations for ships. BB=battleship, CA=heavy cruiser, CL=light cruiser, DD=Destroyer, DE= destroyer escort, and there are others.
BTW, I am definitely a follower of Mahan. 8-)

Maybe a bit late, but I'll add it anyway

These are essentially the designations I'm using in my upcoming Starmada universe setting. They are not set-in-stone and revolve more around the role of the ship rather than its physical size.

By order in the fleet list:
Gunboat - A lightly armed police ship intended for nothing more than local system patrol.

Corvette - Fast, inexpensive and lightly armed patrol ship. Designed for pirate interdiction (pirates play heavily in my setting) and convoy escort. Should operate in packs. Usually employed by militias or corporations.

Frigate - Generally the smallest Navy ships. Used for convoy escort, patrol, and system interdiction. Hyperspace coils are too small to use for effective scouting.

Destroyer - Smallest ship used in fleet actions. Destroyers in my universe are usually specialized to fill specific roles, such as escort, skirmishing, or scouting. Also generally the smallest ship capable of operating independently.

Light Cruiser - Most common Navy warship. Offers the best compromise between cost-to-operate, weapons, defenses, and speed. Various models exist to fill different roles.

Cruiser - Standard Navy warship. A Navy patrol group is usually made up of a cruiser with several light cruisers and various amounts of smaller escort ships. In battle a cruiser is suppose to dish out and absorb damage, and specifically keep the attention of the enemy cruisers off the light cruisers (while they chew apart the hostile forces). Cruiser are generally the largest Navy ships used outside of wartime.

Battlecruiser/Heavy Cruiser - Essentially an upgunned cruiser, usually with more protection and armament. Somewhat more rare because of the cost in both material and logistics. Not designed to fill a particular role, more to counter the increasing number of cruisers. Not generally deployed outside of wartime.

Grand Cruiser/Stardreadnaught - Experimental starships designed to bring overwhelming, decisive firepower to a battle. About 50% larger than a cruiser. At the current point in my timeline none have been deployed in active duty, though several prototypes exist. Warships of this size have not been built due mostly to the cost and logistical requirements.

Other Designations:

Raider - Small, fast starship used mostly by pirates. Heavily armed for their size. Usually very weak hulls as their maintenance and build quality is highly suspect.

Warcruiser - General designation given to any ship with firepower comparable to a Navy fleet warship.

Escort - General designation given to any ship designed primarily for convoy protection.

System Monitor - Usually a small ship (can be purpose built but often a conversion) that is slow but very heavily armed. Designed to defend static locations like space stations. Doesn't often have a hyperdrive to cut down on used mass. In battle a system monitor is considered "successful" if it manages to get its weapons fire off before being blown to bits.

That's basically where most of my designations fit. They're based more around role rather than size, so it's possible to have a "destroyer" that's equivalent to light cruiser tonnage, for example.

(if anyone is wondering about size, my cruisers sit at 16-18 hull, 7-8 armour, and a speed between 3-5)

That's a decent size. From what I've been reading around here it looks like my ships are "small", relatively speaking, but I think that works well into my timeline as it takes place somewhat "earlier" than most space operas. I think that gives my universe lots of room for ships to grow as I add more technology and ship types, without having to worry too much about hull creep.

I've always liked the Babylon 5 universe and its proliferation of ship classifications.  The best example is the Earth Alliance Omega destroyer, which out masses the Earth Alliance Nova Dreadnought (something you don't see too often).  Some of the other races have similar flips in the traditional (by this I mean WW1-WWII) order.  Given that such flips have happened in the past it makes for a neat little insiders joke.

Most of the ships I design vary in size by their assigned roles and I don't worry about size (hull or SU) vs. name.  It also varies by tech level obviously.  My Narn Battleships have the same hull as my BFG light cruisers, for instance.  In my group we usually simply designate each ship as being of a certain points value (After the Tyranid Kraken 60hull/40Armor 200point regenerating ship incident anyway)