dyeing vs staining

dyeing and staining both are nouns.

Word	Noun	Adjective	Verb	Adverb
dyeing	Yes	No	No	No
staining	Yes	No	No	No

As nouns, staining is a hyponym of dyeing; that is, staining is a word with a more specific, narrower meaning than dyeing:

dyeing: the use of dye to change the color of something permanently
staining: (histology) the use of a dye to color specimens for microscopic study

dyeing (noun)	staining (noun)
the use of dye to change the color of something permanently	(histology) the use of a dye to color specimens for microscopic study
	the act of spotting or staining something