The words infer, and imply. Can have several comparable meanings, Imply means to basically say something indirectly. If I was to highlight a summary of a chapter I could imply many things. Implying also derives from the fact that, it is opinion or a conclusion resulted from some sort of reasoning. The result of implying something also depends on the interpreter, the person that is hearing or watching what you do. So it boils down to interpretation.
Infer, means to say something indirectly just as to imply. But with a somewhat stronger directness. Example, imagine 3 people, when you imply something. It is as if you’re having a middleman speak for you. The middleman symbolizes the interpretation, before it gets to the other person. When you infer, the person is less likely to use the middle man. It in some ways is like imply means to hide behind a mask. As to infer means to remove apart of the mask. How they are alike is in the root meaning.
They are both alike in the root meaning. They both are indirect ways of saying something. Both are ways of saying something without really saying it. Where they are different, Is when there is no interpretation, or when there is multiple ways to interpret something.