battledore vs badminton

battledore and badminton both are nouns.

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

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

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

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