Predictive control is a general term that refers to a class of control strategies where the controller makes decisions based on predictions of future system behavior. Although Predictive control and Model Predictive Control (MPC) are terms that have been used as synonyms in literature, MPC originally involves the use of an optimization function aligned with a constrained dynamical system that simulates the process that is being controlled.
(Source: MathWorks)
Predictive control is a broader term that includes other approaches like data-based learning techniques that are used to predict the behaviour of control targets like regression models and machine learning methods. The use of data-driven models is more common on situations where it is hard to build a good model given large and complex processes involved.
(Source: Predictive control of a water distribution system based on process historian data)