ex-president vs president

ex-president and president both are nouns.

Word	Noun	Adjective	Verb	Adverb
ex-president	Yes	No	No	No
president	Yes	No	No	No

As nouns, president is a hypernym of ex-president; that is, president is a word with a broader meaning than ex-president:

ex-president (noun)	president (noun)
a former president	the chief executive of a republic
	an executive officer of a firm or corporation
	the head administrative officer of a college or university
	the officer who presides at the meetings of an organization