battledore vs battledore and shuttlecock

battledore and battledore and shuttlecock both are nouns.

Word	Noun	Adjective	Verb	Adverb
battledore	Yes	No	No	No
battledore and shuttlecock	Yes	No	No	No

As nouns, battledore and battledore and shuttlecock are synonyms defined as:

battledore (noun)	battledore and shuttlecock (noun)
an ancient racket game	an ancient racket game
a light long-handled racket used by badminton players