badminton racket vs badminton racquet

badminton racket and badminton racquet both are nouns.

Word	Noun	Adjective	Verb	Adverb
badminton racket	Yes	No	No	No
badminton racquet	Yes	No	No	No

As nouns, badminton racket and badminton racquet are synonyms defined as:

badminton racket and badminton racquet: a light long-handled racket used by badminton players

Other synonyms of badminton racket include battledore.

badminton racket (noun)	badminton racquet (noun)
a light long-handled racket used by badminton players	a light long-handled racket used by badminton players