pencil eraser vs eraser

pencil eraser and eraser both are nouns.

Word	Noun	Adjective	Verb	Adverb
pencil eraser	Yes	No	No	No
eraser	Yes	No	No	No

As nouns, eraser is a hypernym of pencil eraser; that is, eraser is a word with a broader meaning than pencil eraser:

pencil eraser: an eraser made of rubber (or of a synthetic material with properties similar to rubber); commonly mounted at one end of a pencil
eraser: an implement used to erase something

pencil eraser (noun)	eraser (noun)
an eraser made of rubber (or of a synthetic material with properties similar to rubber); commonly mounted at one end of a pencil	an implement used to erase something