supreme headquarters vs high command

supreme headquarters and high command both are nouns.

Word	Noun	Adjective	Verb	Adverb
supreme headquarters	Yes	No	No	No
high command	Yes	No	No	No

As nouns, supreme headquarters and high command are synonyms defined as:

supreme headquarters and high command: the highest leaders in an organization (e.g. the commander-in-chief and senior officers of the military)

supreme headquarters (noun)	high command (noun)
the highest leaders in an organization (e.g. the commander-in-chief and senior officers of the military)	the highest leaders in an organization (e.g. the commander-in-chief and senior officers of the military)