telephone company vs phone company

telephone company and phone company both are nouns.

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

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

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

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

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