distinction vs have the distinction

distinction is a noun but have the distinction is not a noun.

Word	Noun	Adjective	Verb	Adverb
distinction	Yes	No	No	No
have the distinction	No	No	Yes	No

distinction (noun)	have the distinction (noun)
a distinguishing difference between similar things or people
a discrimination between things as different and distinct on the basis of their characteristics or attributes
an honor awarded to someone in recognition of achievement or superiority
high status importance owing to marked superiority

distinction (verb)	have the distinction (verb)
	be distinguished from others of a similar type by virtue of a notable characteristic