rocking chair vs rocker

rocking chair and rocker both are nouns.

Word	Noun	Adjective	Verb	Adverb
rocking chair	Yes	No	No	No
rocker	Yes	No	No	No

As nouns, rocking chair and rocker are synonyms defined as:

rocking chair (noun)	rocker (noun)
a chair mounted on rockers	a curved support that permits the supported object to rock to and fro
	a chair mounted on rockers
	an ice skate with a curved blade
	a trough that can be rocked back and forth; used by gold miners to shake auriferous earth in water in order to separate the gold
	a teenager or young adult in the 1960s who wore leather jackets and rode motorcycles
	a performer or composer or fan of rock music
	an attendant who rocks a child in a cradle