private line vs telephone line

private line and telephone line both are nouns.

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

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

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

private line (noun)	telephone line (noun)
a telephone line serving a single subscriber	a telephone connection
	the wire that carries telegraph and telephone signals