Both prediction and inference refer to guessing what happens in the future. The main difference is that a prediction is foretelling the future event or occurrence; however, the word inference is also a similar concept, but with the presence of reason, logic, and deduction.
The inference is arriving at a conclusion based upon tangible evidence, while a prediction is coming t a conclusion without any physical evidence or information. Inference can also mean hinting around something, or researched speculation, whereas a prediction is arrived at through unresearched speculation.