These two describe opposite ends of a single transaction, which is why swapping them is more than a spelling slip — it reverses who did what. A speaker implies by suggesting something without stating it. A listener infers by working it out. Mix them up in an account of a conversation and you have changed who said what, which in a minute or a witness statement is not a small thing.
A verb. To suggest something without saying it directly. Done by the person producing the message.
A verb. To work something out from evidence or hints. Done by the person receiving the message.
Quick way to remember
Ask who is doing it. The person sending the message implies — both start with sounds you make outward. The person receiving it infers — think "in," taking the meaning in. A speaker cannot infer their own hint, and a listener cannot imply what they were told.