Imply means that someone wants to make something understood without expressing it directly. It is safe to say that this technique is used often by politicians.
Synonyms: hint, suggest, insinuate, point toward.
Infer means that the hearer perceives or concludes something.
Synonyms: assume, deduce, judge, suppose, gather, conjecture, surmise, understand, extrapolate, reckon, and reason.
Examples: The jurors listened carefully, and all inferred that the witness was lying…I listened to Dan Rather’s interview and inferred that the politician would never be forthcoming.
One university writing lab says, “You imply things through your own words. You infer things from someone else’s words.” The speaker implies. The listener infers.