cigarette holder vs holder

cigarette holder and holder both are nouns.

Word	Noun	Adjective	Verb	Adverb
cigarette holder	Yes	No	No	No
holder	Yes	No	No	No

As nouns, holder is a hypernym of cigarette holder; that is, holder is a word with a broader meaning than cigarette holder:

Other hypernyms of cigarette holder include tube, tubing.

cigarette holder (noun)	holder (noun)
a tube that holds a cigarette while it is being smoked	a holding device
	the person who is in possession of a check or note or bond or document of title that is endorsed to him or to whoever holds it
	a person who holds something