private property vs personal property

private property and personal property both are nouns.

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

As nouns, private property and personal property are synonyms defined as:

private property and personal property: movable property (as distinguished from real estate)

Other synonyms of private property include personal estate, personalty.

private property (noun)	personal property (noun)
movable property (as distinguished from real estate)	movable property (as distinguished from real estate)