white man's burden vs duty

white man's burden and duty both are nouns.

Word	Noun	Adjective	Verb	Adverb
white man's burden	Yes	No	No	No
duty	Yes	No	No	No

As nouns, duty is a hypernym of white man's burden; that is, duty is a word with a broader meaning than white man's burden:

white man's burden: the supposed responsibility of the white race to provide care for their non-white subjects
duty: the social force that binds you to the courses of action demanded by that force

Other hypernyms of white man's burden include obligation, responsibility.

white man's burden (noun)	duty (noun)
the supposed responsibility of the white race to provide care for their non-white subjects	the social force that binds you to the courses of action demanded by that force
	work that you are obliged to perform for moral or legal reasons
	a government tax on imports or exports