cutter vs cigar cutter

cutter and cigar cutter both are nouns.

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

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

Other hyponyms of cutter include bolt cutter, die, edge tool, glass cutter, tile cutter.

cutter (noun)	cigar cutter (noun)
a cutting implement; a tool for cutting	an implement for cutting the tip off of a cigar
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