badminton vs battledore

badminton and battledore both are nouns.

Word	Noun	Adjective	Verb	Adverb
badminton	Yes	No	No	No
battledore	Yes	No	No	No

As nouns, battledore is a hyponym of badminton; that is, battledore is a word with a more specific, narrower meaning than badminton:

badminton: a game played on a court with light long-handled rackets used to volley a shuttlecock over a net
battledore: an ancient racket game

Other hyponyms of badminton include battledore and shuttlecock, singles, doubles.

badminton (noun)	battledore (noun)
a game played on a court with light long-handled rackets used to volley a shuttlecock over a net	an ancient racket game
	a light long-handled racket used by badminton players