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From Citizendium, the Citizens' Compendium
Primarily a term used for United States ocean escort warships in World War II, a destroyer escort is a slower, less heavily armed version of a destroyer, optimized for low cost. With the naval vessel designation code DE, the current equivalent in the U.S. Navy is called a frigate, a term that is used with very many meanings. The U.S. built six main classes of DE in WWII. 
Many were given to other navies after the war.
The typical WWII DE had 3" main guns rather than the 5"-38 caliber guns of fleet destroyers, although some classes had 5". They had a maximum speed in the mid 20 knot range rather than the mid-thirties, and a lighter displacement. They were primarily anti-submarine warfare and, to a lesser extent, anti-air warfare vessels, with very limited anti-surface warfare capability. In extreme situations, however, they formed key parts of an air defense screen, such as radar pickets at the Battle of Okinawa, or joined destroyers in attacks on major surface warships in the Action off Samar.
A number were converted to fast transports (APD), with more weapons but less transport capacity than attack cargo ships. Some were given extra radar.
Several DE classes were built after WWII, but were eventually redesignated frigates (FF). The early versions were inadequate to deal with Soviet submarines; the eventual later frigate types, such as the Knox-class or current Oliver Hazard Perry-class are quite capable ships by WWII standards.