headache vs head ache

headache and head ache both are nouns.

Word	Noun	Adjective	Verb	Adverb
headache	Yes	No	No	No
head ache	Yes	No	No	No

As nouns, headache and head ache are synonyms defined as:

headache and head ache: pain in the head caused by dilation of cerebral arteries or muscle contractions or a reaction to drugs

Other synonyms of headache include cephalalgia.

headache (noun)	head ache (noun)
something or someone that causes anxiety; a source of unhappiness	pain in the head caused by dilation of cerebral arteries or muscle contractions or a reaction to drugs
pain in the head caused by dilation of cerebral arteries or muscle contractions or a reaction to drugs