head count vs count

head count and count both are nouns.

Word	Noun	Adjective	Verb	Adverb
head count	Yes	No	No	No
count	Yes	No	Yes	No

As nouns, count is a hypernym of head count; that is, count is a word with a broader meaning than head count:

head count (noun)	count (noun)
number of people in a particular group	the act of counting; reciting numbers in ascending order
	a nobleman (in various countries) having rank equal to a British earl
	the total number counted

head count (verb)	count (verb)
	include as if by counting
	have faith or confidence in
	take account of
	determine the number or amount of
	name or recite the numbers in ascending order
	show consideration for; take into account
	have weight; have import, carry weight
	put into a group
	have a certain value or carry a certain weight