Elicit is a verb: to draw out a response or reaction — the question elicited a laugh. Illicit is an adjective: illegal or forbidden — illicit trade. They sound identical in speech, so the difference only appears in writing, and one of them is a verb where the other cannot be.
The core difference
A verb and an adjective that happen to be homophones.
- elicit (verb) — draw out: elicit a confession, elicit sympathy.
- illicit (adjective) — unlawful: illicit substances, an illicit affair.
The test
If it is doing something, it is elicit. If it is describing something, it is illicit. You cannot illicit a response, and there is no such thing as an elicit deal.
The roots
Elicit is from Latin elicere, to draw out. Illicit is in- (not) plus licitus (permitted) — the same root as licence. The negating il- is the giveaway: it marks the word that means "not allowed".