contradictory vs self-contradictory

contradictory is a noun but self-contradictory is not a noun.

Word	Noun	Adjective	Verb	Adverb
contradictory	Yes	Yes	No	No
self-contradictory	No	Yes	No	No

As adjectives, contradictory and self-contradictory are synonyms defined as:

Other synonyms of contradictory include at odds, conflicting.

contradictory (noun)	self-contradictory (noun)
two propositions are contradictories if both cannot be true (or both cannot be false) at the same time

contradictory (adjective)	self-contradictory (adjective)
of words or propositions so related that both cannot be true and both cannot be false	in disagreement
unable for both to exist or be true at the same time	seemingly contradictory but nonetheless possibly true
in disagreement
that confounds or contradicts or confuses