illation vs analogy

illation and analogy both are nouns.

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

As nouns, analogy is a hyponym of illation; that is, analogy 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
analogy: an inference that if things agree in some respects they probably agree in others

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

illation (noun)	analogy (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	drawing a comparison in order to show a similarity in some respect
	an inference that if things agree in some respects they probably agree in others
	the religious belief that between creature and creator no similarity can be found so great but that the dissimilarity is always greater; any analogy between God and humans will always be inadequate