paint vs finger-paint

paint is a noun but finger-paint is not a noun.

Word	Noun	Adjective	Verb	Adverb
paint	Yes	No	Yes	No
finger-paint	No	No	Yes	No

As verbs, finger-paint is a hyponym of paint; that is, finger-paint is a word with a more specific, narrower meaning than paint:

Other hyponyms of paint include stipple, bodypaint, fresco, distemper, charge, fill in, shade, stipple, watercolor, watercolour.

paint (noun)	finger-paint (noun)
a substance used as a coating to protect or decorate a surface (especially a mixture of pigment suspended in a liquid); dries to form a hard coating
makeup consisting of a pink or red powder applied to the cheeks
(basketball) a space (including the foul line) in front of the basket at each end of a basketball court; usually painted a different color from the rest of the court

paint (verb)	finger-paint (verb)
apply paint to; coat with paint	apply colors with one's fingers
apply a liquid to; e.g., paint the gutters with linseed oil
make a painting of
make a painting