headache vs burden

headache and burden both are nouns.

Word	Noun	Adjective	Verb	Adverb
headache	Yes	No	No	No
burden	Yes	No	Yes	No

As nouns, burden is a hyponym of headache; that is, burden is a word with a more specific, narrower meaning than headache:

Other hyponyms of headache include bugaboo, encumbrance, incumbrance, load, onus, business.

headache (noun)	burden (noun)
something or someone that causes anxiety; a source of unhappiness	weight to be borne or conveyed
pain in the head caused by dilation of cerebral arteries or muscle contractions or a reaction to drugs	the central idea that is expanded in a document or discourse
	an onerous or difficult concern
	the central meaning or theme of a speech or literary work

headache (verb)	burden (verb)
	impose a task upon, assign a responsibility to
	weight down with a load