privately held corporation vs private corporation

privately held corporation and private corporation both are nouns.

Word	Noun	Adjective	Verb	Adverb
privately held corporation	Yes	No	No	No
private corporation	Yes	No	No	No

As nouns, privately held corporation and private corporation are synonyms defined as:

privately held corporation and private corporation: a corporation owned by a few people; shares have no public market

Other synonyms of privately held corporation include close corporation, closed corporation.

privately held corporation (noun)	private corporation (noun)
a corporation owned by a few people; shares have no public market	a corporation owned by a few people; shares have no public market