Turkmen vs Turkic

Turkmen and Turkic both are nouns.

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

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

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

Turkmen (noun)	Turkic (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 (adjective)
of or relating to or characteristic of Turkmenistan or its people or culture	of or relating to the people who speak the Turkic language