private property vs holding

private property and holding both are nouns.

Word	Noun	Adjective	Verb	Adverb
private property	Yes	No	No	No
holding	Yes	No	No	No

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

private property: movable property (as distinguished from real estate)
holding: something owned; any tangible or intangible possession that is owned by someone

Other hypernyms of private property include belongings, property.

private property (noun)	holding (noun)
movable property (as distinguished from real estate)	the act of retaining something
	something owned; any tangible or intangible possession that is owned by someone