Mongolian vs Khalkha

Mongolian and Khalkha both are nouns.

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

As nouns, Khalkha is a hyponym of Mongolian; that is, Khalkha is a word with a more specific, narrower meaning than Mongolian:

Mongolian: a family of Altaic language spoken in Mongolia
Khalkha: the language of the Khalkha that is the official language of the Mongolian People's Republic

Other hyponyms of Mongolian include Kalka, Kalka language, Khalka, Khalka language, Khalkha language.

As nouns, Khalkha is a hyponym of Mongolian; that is, Khalkha is a word with a more specific, narrower meaning than Mongolian:

Mongolian: a member of the nomadic peoples of Mongolia
Khalkha: the Mongol people living in the central and eastern parts of Outer Mongolia

Other hyponyms of Mongolian include Mongol Tatar, Tartar, Tatar, Kalka, Khalka.

Mongolian (noun)	Khalkha (noun)
a family of Altaic language spoken in Mongolia	the language of the Khalkha that is the official language of the Mongolian People's Republic
a member of the nomadic peoples of Mongolia	the Mongol people living in the central and eastern parts of Outer Mongolia

Mongolian (adjective)	Khalkha (adjective)
of or relating to the region of Mongolia or its people or their languages or cultures
of or relating to the modern Mongolian People's Republic