pepper grinder vs mill

pepper grinder and mill both are nouns.

Word	Noun	Adjective	Verb	Adverb
pepper grinder	Yes	No	No	No
mill	Yes	No	Yes	No

As nouns, mill is a hypernym of pepper grinder; that is, mill is a word with a broader meaning than pepper grinder:

Other hypernyms of pepper grinder include grinder, milling machinery.

pepper grinder (noun)	mill (noun)
a mill for grinding pepper	the act of grinding to a powder or dust
	machinery that processes materials by grinding or crushing
	a plant consisting of one or more buildings with facilities for manufacturing

pepper grinder (verb)	mill (verb)
	grind with a mill
	produce a ridge around the edge of
	roll out (metal) with a rolling machine
	move about in a confused manner