hair dye vs dyestuff

hair dye and dyestuff both are nouns.

Word	Noun	Adjective	Verb	Adverb
hair dye	Yes	No	No	No
dyestuff	Yes	No	No	No

As nouns, dyestuff is a hypernym of hair dye; that is, dyestuff is a word with a broader meaning than hair dye:

hair dye: a dye for coloring the hair
dyestuff: a usually soluble substance for staining or coloring e.g. fabrics or hair

Other hypernyms of hair dye include dye.

hair dye (noun)	dyestuff (noun)
a dye for coloring the hair	a usually soluble substance for staining or coloring e.g. fabrics or hair