Most times, people use both imply and infer interchangeably as though they are the same, but the truth is that both words are not totally the same. Imply is a verb which means to suggest by logical interference. For example: when I state that your son is nice, I am not implying that all children are nice.
The word implies can only be used by a speaker, and that gives a speaker the chance to clarify his earlier statement. However, if the word is to be used by another person other than the speaker, it will always be in the form of a question.
For example: Are you implying that our leaders have failed us. On the other hand, infer means to conclude by making a deduction out of a particular message. For example, I think we should infer from what the principal said that we could graduate with good grades. The word infers usually used by a listener to react to what has been said.