To me, "projecting" is taking a possible scenario (real or imagined) and allowing yourself to run wild with what-ifs. "Predicting" is forecasting the outcome of a situation based on the facts or conditions known to you.
Projecting: Oh my gosh, what are we gonna do if it rains on our parade tomorrow? It might flood. We'll need boats. People might drown.
Predicting: Well, the skies are dark and cloudy. I think we can expect rain.