pigeon hawk vs falcon

pigeon hawk and falcon both are nouns.

Word	Noun	Adjective	Verb	Adverb
pigeon hawk	Yes	No	No	No
falcon	Yes	No	Yes	No

As nouns, falcon is a hypernym of pigeon hawk; that is, falcon is a word with a broader meaning than pigeon hawk:

pigeon hawk: small falcon of Europe and America having dark plumage with black-barred tail; used in falconry
falcon: diurnal birds of prey having long pointed powerful wings adapted for swift flight

pigeon hawk (noun)	falcon (noun)
small falcon of Europe and America having dark plumage with black-barred tail; used in falconry	diurnal birds of prey having long pointed powerful wings adapted for swift flight

pigeon hawk (verb)	falcon (verb)
	hunt with falcons