head for the hills vs go away

head for the hills and go away both are verbs.

Word	Noun	Adjective	Verb	Adverb
head for the hills	No	No	Yes	No
go away	No	No	Yes	No

As verbs, go away is a hypernym of head for the hills; that is, go away is a word with a broader meaning than head for the hills:

Other hypernyms of head for the hills include go forth, leave.

head for the hills (verb)	go away (verb)
flee; take to one's heels; cut and run	get lost, as without warning or explanation
	go away from a place
	move away from a place into another direction
	become invisible or unnoticeable