modal verb vs modal auxiliary

modal verb and modal auxiliary both are nouns.

Word	Noun	Adjective	Verb	Adverb
modal verb	Yes	No	No	No
modal auxiliary	Yes	No	No	No

As nouns, modal verb and modal auxiliary are synonyms defined as:

modal verb and modal auxiliary: an auxiliary verb (such as `can' or `will') that is used to express modality

Other synonyms of modal verb include modal, modal auxiliary verb.

modal verb (noun)	modal auxiliary (noun)
an auxiliary verb (such as `can' or `will') that is used to express modality	an auxiliary verb (such as `can' or `will') that is used to express modality