personal property vs private property

personal property and private property both are nouns.

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

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

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

Other synonyms of personal property include personal estate, personalty.

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