eraser vs pencil eraser

eraser and pencil eraser both are nouns.

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

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

eraser: an implement used to erase something
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

Other hyponyms of eraser include blackboard eraser, ink eraser, rubber, rubber eraser.

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