illation vs corollary

illation and corollary both are nouns.

Word	Noun	Adjective	Verb	Adverb
illation	Yes	No	No	No
corollary	Yes	No	No	No

As nouns, corollary is a hyponym of illation; that is, corollary is a word with a more specific, narrower meaning than illation:

illation: the reasoning involved in drawing a conclusion or making a logical judgment on the basis of circumstantial evidence and prior conclusions rather than on the basis of direct observation
corollary: (logic) an inference that follows directly from the proof of another proposition

Other hyponyms of illation include analogy, derivation, deduction, entailment, implication, extrapolation, presumption.

illation (noun)	corollary (noun)
the reasoning involved in drawing a conclusion or making a logical judgment on the basis of circumstantial evidence and prior conclusions rather than on the basis of direct observation	(logic) an inference that follows directly from the proof of another proposition
	a practical consequence that follows naturally