smoker vs cigar smoker

smoker and cigar smoker both are nouns.

Word	Noun	Adjective	Verb	Adverb
smoker	Yes	No	No	No
cigar smoker	Yes	No	No	No

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

Other hyponyms of smoker include chain-smoker, cigarette smoker, pipe smoker.

smoker (noun)	cigar smoker (noun)
a passenger car for passengers who wish to smoke	a smoker of cigars
a party for men only (or one considered suitable for men only)
a person who smokes tobacco