After doing some research I have come to the following conclusions with regards to 20th Century Naval Ship types.
Battleship: Ship capable of standing in the battle Line against all comers.
Cruiser: Long Ranged, multi-role ship. Designed to screen battleships, raid commerce, shore bombardment, blockade enemy ports and go on long patrols.
Destroyer, Multi-role Escort designed to keep up with the fleet. Designed to attack heavier ships. Designed to screen friendly forces from enemy Destroyers and smaller ships. ASW role. Air Defense Role. Limited Shore Bombardment.
Destroyer-Escort/Frigate: Same class of ship two different names. Originally designed to fullfill the role of escorting Merchantmen. Capable of short bursts of speed after attacking a detected submarine or other screening duties so it could catch back up to the merchants it was escorting. Primarily ASW platform but later versions multi-role. (Usually with limited Surface warfare capability.)
Corvette: Same basic mission as the Frigate on a smaller more specialized platform. Primarily ASW.
Translating to Traveller.
Battleship/Drednaught: Attack enemy ships in outright battle.
Cruiser: Screen Battleships, perform independent missions, commerce raiding, long range patrols, etc.
Destroyer/Fleet Escort: (3Kton-8Kton) Smallest ship actually deployed to screen a fleet. Smallest ship that operational requirements require the same jump and maneuver capability as the rest of the fleet.
<Edit:> Notice I said require the same jump and maneuver capability, that doesn't mean that the smaller escorts, listed below, won't have the same capabilities, some will, some won't but operationally they aren't required to have them. </Edit>
Destroyer-Escort/Frigate: (1000-2000 Tons) Commerce escort.
Corvette: Small escorts, generally under 1000 tons. (Patrol Cruiser, Mercenary Cruiser, Lucifer, Valor, Zhidts, etc.)