implicit (adj.) implied or hinted at example: There was a threat implicit in his request.
imply (v.) to hint or express indirectly example: Glaring at me, she implied that I was in big trouble.
infer (v.) to draw a conclusion or make a deduction example: I infer from your expression that you are upset. example: By standing by the door, I implied that it was time for him to leave.
You can draw an inference from someone else’s implication, not vice versa.
The speaker implies and the listener infers.