mover vs puller

mover and puller both are nouns.

Word	Noun	Adjective	Verb	Adverb
mover	Yes	No	No	No
puller	Yes	No	No	No

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

mover: someone who moves
puller: someone who applies force so as to cause motion toward herself or himself

mover (noun)	puller (noun)
a company that moves the possessions of a family or business from one site to another	someone who pulls or tugs or drags in an effort to move something
someone who moves	someone who applies force so as to cause motion toward herself or himself
(parliamentary procedure) someone who makes a formal motion
workman employed by a moving company