A bit unclear what you are asking. Presumably only English-language armies would use English words. But more generally,
Going into the Second World War, the [U.S.] Cavalry consisted of three
Regular, four National Guard, and six Organized Reserve cavalry
divisions as well as the independent 56th Cavalry Brigade. Because of
a shortage of men, on 15 July 1942, the 2d Cavalry Division was
inactivated to permit organization of the 9th Armored Division. White
cavalrymen were assigned to the 9th Armored Division, and the
all-black 4th Cavalry Brigade became a nondivisional formation.
(wikipedia)
In October 1928, a new era began as the [British] 11th Hussars became the
first regular cavalry regiment to "mechanise", to change from a horsed
cavalry role to a motorised one, re-equipping with armoured cars
previously used by the Royal Tank Corps. Other regiments followed
suit; in April 1939, the Royal Armoured Corps was formed to encompass
the eighteen mechanised cavalry regiments of the line alongside the
eight battalions of the Royal Tank Regiment
(wikipedia)
The [German] 1st Cavalry Division was formed in October 1939. It
fought in the Netherlands, Belgium, France and on the Eastern Front.
It was officially transformed into the 24th Panzer Division in late
1941.
(wikipedia)