Turkmen vs Turkic language

Turkmen and Turkic language both are nouns.

Word	Noun	Adjective	Verb	Adverb
Turkmen	Yes	Yes	No	No
Turkic language	Yes	No	No	No

As nouns, Turkic language is a hypernym of Turkmen; that is, Turkic language is a word with a broader meaning than Turkmen:

Other hypernyms of Turkmen include Turki, Turkic, Turko-Tatar.

Turkmen (noun)	Turkic language (noun)
the Turkic language spoken by the Turkoman	a subfamily of Altaic languages
a republic in Asia to the east of the Caspian Sea and to the south of Kazakhstan and to the north of Iran; an Asian soviet from 1925 to 1991
a member of a Turkic people living in Turkmenistan and neighboring areas

Turkmen (adjective)	Turkic language (adjective)
of or relating to or characteristic of Turkmenistan or its people or culture