modal verb vs auxiliary verb

modal verb and auxiliary verb both are nouns.

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

As nouns, auxiliary verb is a hypernym of modal verb; that is, auxiliary verb is a word with a broader meaning than modal verb:

modal verb: an auxiliary verb (such as `can' or `will') that is used to express modality
auxiliary verb: a verb that combines with another verb in a verb phrase to help form tense, mood, voice, or condition of the verb it combines with

modal verb (noun)	auxiliary verb (noun)
an auxiliary verb (such as `can' or `will') that is used to express modality	a verb that combines with another verb in a verb phrase to help form tense, mood, voice, or condition of the verb it combines with