I found a very nice explanation online that tells the difference between the words infer and imply: “You imply things through your own words. You infer things from someone else’s words.” The speaker implies. The listener infers (gets it).
When you imply something, you are initiating the action. You might be saying something that is implying something hidden in the subtext. By pointing at that chocolate bar on the rack, I’m implying to my husband that I’d like him to put one (or more) in the shopping basket. When you imply, you express something indirectly.
However, when you infer something, you are surmising, extrapolating, or deducing something from what you see or hear (or taste, smell, or touch). You experience something through your senses and you infer what it might be or mean. You might infer that I’m lying when I say I hate chocolate. Especially if you see all the chocolate in my cupboards and on the counters. When you tell me that, I might imply you’re being a bit rude. You might then infer that I’m somewhat defensive, if not dissembling. And then I might imply it would be a good idea for you to leave my house. And so on . . .