Projections are substantively different than predictions, even if both are concerned with a vision of the future. By way of illustration, let’s consider their Latin origins.
The word projection is derived from pro (meaning “for”) and the verb iacere (“to throw”). Prediction, meanwhile, is a composite of pre (“before”) and dīcere (“to say”).
What does this reveal? Nothing, really — except, perhaps, that etymological analysis is of limited utility in some cases.