The term "probability wave" isn't very precise, so its hard to say if the two are related. As Pete says, the quantum field describes the quantum nature of fields, such as the electromagnetic field. It also describes particles, such as electrons, as excitations of a field. Fundamentally, all our theories try to describe what we can observe, and quantum fields describe possible observations in terms of probabilities of making those observations. So in a sense, the quantum fields are "probability fields" in the sense that at the end of the day, you calculate the probabilities of making different observations.

The quantum nature of the universe means that somehow probability is fundamental. Even if we know everything possible about the universe, the best we can do is to describe the probabilities of different observations. We can't know for certain what the outcome of an experiment will be.