I've been wrestling with what to call the outputs of my models - forecasts or predictions. Whenever I have one of this epistemic debates with myself, my writing suffers because I start using the terms interchangeably, much to the detriment of clarity. I just stumbled across an old Webzine article on one view of the distinction between these terms, from of all people, a weather guy - Mike MacCraken. Or actually a climate guy. Anyway - interesting viewpoint that essentially makes a forecast conditional on the person making it - independent of how they arrived at the forecast. Thus one key difference is that the prediction is conditional on the methods. If a mathematical model is used then if the assumptions are true, then the conclusion is true. Can't argue with that. But when a prediction is used to make a forecast, then the credibility of the person making the assumptions comes into play.
Food for thought. Still don't know whether to use forecast or prediction.