Irish language vs Irish Gaelic language

Irish language and Irish Gaelic language both are nouns.

Word	Noun	Adjective	Verb	Adverb
Irish language	Yes	No	No	No
Irish Gaelic language	Yes	No	No	No

As nouns, Irish language and Irish Gaelic language are synonyms defined as:

Irish language and Irish Gaelic language: the Celtic language of Ireland

Other synonyms of Irish language include Irish, Irish Gaelic.

Irish language (noun)	Irish Gaelic language (noun)
the Celtic language of Ireland	the Celtic language of Ireland