washing vs household linen

washing and household linen both are nouns.

Word	Noun	Adjective	Verb	Adverb
washing	Yes	No	No	No
household linen	Yes	No	No	No

As nouns, household linen is a hypernym of washing; that is, household linen is a word with a broader meaning than washing:

washing: garments or white goods that can be cleaned by laundering
household linen: drygoods for household use that are typically made of white cloth

Other hypernyms of washing include garment, white goods.

washing (noun)	household linen (noun)
the work of cleansing (usually with soap and water)	drygoods for household use that are typically made of white cloth
garments or white goods that can be cleaned by laundering