Hello
"predict" is actually a synonym for "anticipate".
But I would say, depending on the context, that to "predict" means to say with certainty that something specific is going to happen in the future or that something will happen as a consequence of something else.
I would also say, depending on the context, that to "anticipate" something is to expect it to happen or to regard it as possible.
So one could say that the difference between these words is the level of probability.
I hope that helps!