badminton racket vs racquet

badminton racket and racquet both are nouns.

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

As nouns, racquet is a hypernym of badminton racket; that is, racquet is a word with a broader meaning than badminton racket:

badminton racket: a light long-handled racket used by badminton players
racquet: a sports implement (usually consisting of a handle and an oval frame with a tightly interlaced network of strings) used to strike a ball (or shuttlecock) in various games

Other hypernyms of badminton racket include racket.

badminton racket (noun)	racquet (noun)
a light long-handled racket used by badminton players	a sports implement (usually consisting of a handle and an oval frame with a tightly interlaced network of strings) used to strike a ball (or shuttlecock) in various games