modal auxiliary vs modal auxiliary verb

modal auxiliary and modal auxiliary verb both are nouns.

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

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

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

Other synonyms of modal auxiliary include modal, modal verb.

modal auxiliary (noun)	modal auxiliary verb (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