chattel vs private property

chattel and private property both are nouns.

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

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

chattel: personal as opposed to real property; any tangible movable property (furniture or domestic animals or a car etc)
private property: movable property (as distinguished from real estate)

Other hypernyms of chattel include personal estate, personal property, personalty.

chattel (noun)	private property (noun)
personal as opposed to real property; any tangible movable property (furniture or domestic animals or a car etc)	movable property (as distinguished from real estate)