In English the word "squadron" tends to be used for larger and "flotilla" for smaller vessels; both may be used for destroyer units.
Similar formations are used in non-English-speaking countries, e.g., the "escadrille"—which would translate directly as "squadron"—in France.
As during World War II, a full-strength DesRon (as it was abbreviated at the time) comprised two Destroyer Divisions or DesDivs of four ships each, plus a squadron flagship; these were operational as well as administrative units.
In the late 1950s and through early 1962 a Squadron (Desron) comprised two four-ship Divisions (Desdivs) with one ship designated the flagship.
The Squadron normally operated as a unit within a Task Group or Fleet, its main duty being as anti-submarine screen for the aircraft carriers.
Cruiser-Destroyer Flotilla Six included Destroyer Squadron Four with USS Johnson in 1971, seemingly home-ported at the Charleston Naval Base.