Italian vs Florentine

Italian and Florentine both are nouns.

Word	Noun	Adjective	Verb	Adverb
Italian	Yes	Yes	No	No
Florentine	Yes	Yes	No	No

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

Italian (noun)	Florentine (noun)
the Romance language spoken in Italy	a native or resident of Florence, Italy
a native or inhabitant of Italy

Italian (adjective)	Florentine (adjective)
of or pertaining to or characteristic of Italy or its people or culture or language	of or relating to or characteristic of the city of Florence, Italy