modal vs modal auxiliary

modal and modal auxiliary both are nouns.

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

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

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

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

modal (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

modal (adjective)	modal auxiliary (adjective)
relating to or expressing the mood of a verb
of or relating to a musical mode; especially written in an ecclesiastical mode
relating to or constituting the most frequent value in a distribution