Implication, inference are often interchangeable, but they may be distinguished when they specifically refer to something that is hinted at but not explicitly stated.
Implication applies to what is hinted, whether the writer or speaker is aware of it or not or whether the reader or hearer recognizes it or not.
When, however, the reader or hearer recognizes what is implied and gathers from it its full significance or makes an explicit statement of it, he has drawn or made an inference.