private line vs subscriber line

private line and subscriber line both are nouns.

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

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

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

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