high command vs leadership

high command and leadership both are nouns.

Word	Noun	Adjective	Verb	Adverb
high command	Yes	No	No	No
leadership	Yes	No	No	No

As nouns, leadership is a hypernym of high command; that is, leadership is a word with a broader meaning than high command:

high command: the highest leaders in an organization (e.g. the commander-in-chief and senior officers of the military)
leadership: the body of people who lead a group

Other hypernyms of high command include leaders.

high command (noun)	leadership (noun)
the highest leaders in an organization (e.g. the commander-in-chief and senior officers of the military)	the activity of leading
	the ability to lead
	the body of people who lead a group
	the status of a leader