property vs quality

property and quality both are nouns.

Word	Noun	Adjective	Verb	Adverb
property	Yes	No	No	No
quality	Yes	Yes	No	No

As nouns, quality is a hyponym of property; that is, quality is a word with a more specific, narrower meaning than property:

property: a construct whereby objects or individuals can be distinguished
quality: a characteristic property that defines the apparent individual nature of something

Other hyponyms of property include character, lineament, characteristic, feature, feature, feature of speech, exactingness.

property (noun)	quality (noun)
any movable articles or objects used on the set of a play or movie	an essential and distinguishing attribute of something or someone
a basic or essential property shared by all members of a class	(music) the distinctive property of a complex sound (a voice or noise or musical sound)
a construct whereby objects or individuals can be distinguished	a degree or grade of excellence or worth
any area set aside for a particular purpose	a characteristic property that defines the apparent individual nature of something
something owned; any tangible or intangible possession that is owned by someone	high social status

property (adjective)	quality (adjective)
	of superior grade
	of high social status