bed linen vs pillowcase

bed linen and pillowcase both are nouns.

Word	Noun	Adjective	Verb	Adverb
bed linen	Yes	No	No	No
pillowcase	Yes	No	No	No

As nouns, pillowcase is a hyponym of bed linen; that is, pillowcase is a word with a more specific, narrower meaning than bed linen:

Other hyponyms of bed linen include case, pillow slip, slip, pillow sham, bed sheet, sheet.

bed linen (noun)	pillowcase (noun)
linen or cotton articles for a bed (as sheets and pillowcases)	bed linen consisting of a cover for a pillow