private enterprise vs economy

private enterprise and economy both are nouns.

Word	Noun	Adjective	Verb	Adverb
private enterprise	Yes	No	No	No
economy	Yes	No	No	No

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

private enterprise: an economy that relies chiefly on market forces to allocate goods and resources and to determine prices
economy: the system of production and distribution and consumption

Other hypernyms of private enterprise include economic system.

private enterprise (noun)	economy (noun)
an economy that relies chiefly on market forces to allocate goods and resources and to determine prices	an act of economizing; reduction in cost
	frugality in the expenditure of money or resources
	the efficient use of resources
	the system of production and distribution and consumption