To predict something is to determine what will happen in the future. When time passes, we will know if the prediction was correct: A prediction can be falsified.
To project something is to determine what a specific model says will happen in the future. A projection is just an informed guess.
Those that predict things will often be wrong, but at least they put their money where their mouth was. And if they analyse why they were wrong, they can make a better prediction next time.