phone service vs telephone company

phone service and telephone company both are nouns.

Word	Noun	Adjective	Verb	Adverb
phone service	Yes	No	No	No
telephone company	Yes	No	No	No

As nouns, phone service and telephone company are synonyms defined as:

phone service and telephone company: a public utility that provides telephone service

Other synonyms of phone service include phone company, telco, telephone service.

phone service (noun)	telephone company (noun)
a public utility that provides telephone service	a public utility that provides telephone service