Old High German vs High German

Old High German and High German both are nouns.

Word	Noun	Adjective	Verb	Adverb
Old High German	Yes	No	No	No
High German	Yes	No	No	No

As nouns, High German is a hypernym of Old High German; that is, High German is a word with a broader meaning than Old High German:

Old High German: High German prior to 1200
High German: the standard German language; developed historically from West Germanic

Other hypernyms of Old High German include German, German language, High German language.

Old High German (noun)	High German (noun)
High German prior to 1200	the standard German language; developed historically from West Germanic