telephone company vs phone service

telephone company and phone service both are nouns.

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

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

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

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

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