pigeon hawk vs Falco columbarius

pigeon hawk and Falco columbarius both are nouns.

Word	Noun	Adjective	Verb	Adverb
pigeon hawk	Yes	No	No	No
Falco columbarius	Yes	No	No	No

As nouns, pigeon hawk and Falco columbarius are synonyms defined as:

pigeon hawk and Falco columbarius: small falcon of Europe and America having dark plumage with black-barred tail; used in falconry

Other synonyms of pigeon hawk include merlin.

pigeon hawk (noun)	Falco columbarius (noun)
small falcon of Europe and America having dark plumage with black-barred tail; used in falconry	small falcon of Europe and America having dark plumage with black-barred tail; used in falconry