printing business vs printing company

printing business and printing company both are nouns.

Word	Noun	Adjective	Verb	Adverb
printing business	Yes	No	No	No
printing company	Yes	No	No	No

As nouns, printing business and printing company are synonyms defined as:

printing business and printing company: a company that does commercial printing

Other synonyms of printing business include printing concern.

printing business (noun)	printing company (noun)
a company that does commercial printing	a company that does commercial printing