Gregorian mode vs musical mode

Gregorian mode and musical mode both are nouns.

Word	Noun	Adjective	Verb	Adverb
Gregorian mode	Yes	No	No	No
musical mode	Yes	No	No	No

As nouns, musical mode is a hypernym of Gregorian mode; that is, musical mode is a word with a broader meaning than Gregorian mode:

Gregorian mode: any of a system of modes used in Gregorian chants up until 1600; derived historically from the Greek mode
musical mode: any of various fixed orders of the various diatonic notes within an octave

Other hypernyms of Gregorian mode include mode.

Gregorian mode (noun)	musical mode (noun)
any of a system of modes used in Gregorian chants up until 1600; derived historically from the Greek mode	any of various fixed orders of the various diatonic notes within an octave