illation vs implication

illation and implication both are nouns.

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

As nouns, implication is a hyponym of illation; that is, implication 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
implication: something that is inferred (deduced or entailed or implied)

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

illation (noun)	implication (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	a meaning that is not expressly stated but can be inferred
	something that is inferred (deduced or entailed or implied)
	an accusation that brings into intimate and usually incriminating connection
	a relation implicated by virtue of involvement or close connection (especially an incriminating involvement)
	a logical relation between propositions p and q of the form `if p then q'; if p is true then q cannot be false