public mover vs moving company

public mover and moving company both are nouns.

Word	Noun	Adjective	Verb	Adverb
public mover	Yes	No	No	No
moving company	Yes	No	No	No

As nouns, public mover and moving company are synonyms defined as:

public mover and moving company: a company that moves the possessions of a family or business from one site to another

Other synonyms of public mover include mover, removal company, removal firm.

public mover (noun)	moving company (noun)
a company that moves the possessions of a family or business from one site to another	a company that moves the possessions of a family or business from one site to another