Mongolian vs Asian

Mongolian and Asian both are nouns.

Word	Noun	Adjective	Verb	Adverb
Mongolian	Yes	Yes	No	No
Asian	Yes	Yes	No	No

As nouns, Asian is a hypernym of Mongolian; that is, Asian is a word with a broader meaning than Mongolian:

Other hypernyms of Mongolian include Asiatic.

Mongolian (noun)	Asian (noun)
a family of Altaic language spoken in Mongolia	a native or inhabitant of Asia
a member of the nomadic peoples of Mongolia

Mongolian (adjective)	Asian (adjective)
of or relating to the region of Mongolia or its people or their languages or cultures	of or relating to or characteristic of Asia or the peoples of Asia or their languages or culture
of or relating to the modern Mongolian People's Republic