puller vs mover

puller and mover both are nouns.

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

As nouns, mover is a hypernym of puller; that is, mover is a word with a broader meaning than puller:

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

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