cigar cutter vs cutter

cigar cutter and cutter both are nouns.

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

As nouns, cutter is a hypernym of cigar cutter; that is, cutter is a word with a broader meaning than cigar cutter:

Other hypernyms of cigar cutter include cutlery, cutting tool.

cigar cutter (noun)	cutter (noun)
an implement for cutting the tip off of a cigar	a cutting implement; a tool for cutting
	a boat for communication between ship and shore
	a sailing vessel with a single mast set further back than the mast of a sloop
	someone whose work is cutting (as e.g. cutting cloth for garments)
	someone who carves the meat
	someone who cuts or carves stone