private line vs phone line

private line and phone line both are nouns.

Word	Noun	Adjective	Verb	Adverb
private line	Yes	No	No	No
phone line	Yes	No	No	No

As nouns, phone line is a hypernym of private line; that is, phone line is a word with a broader meaning than private line:

Other hypernyms of private line include line, subscriber line, telephone circuit, telephone line.

private line (noun)	phone line (noun)
a telephone line serving a single subscriber	a telephone connection