To imply something is not the same as to infer it.
Implication is not the same as inference.
What's the difference?
To imply something is to suggest it without actually stating it. For example, a politician may refuse to deny a statement, implying that it may be true.
To infer something is to conclude that something is true even though the person making the statement has not said it.
So implication comes from the sender of a message while an inference is drawn by the receiver of the message.
The two are clearly related, but not interchangeable.