MCP = Motor CIRCUIT Protector, not "Motor Protector", it is protecting the circuit, not the motor. If there is a GF or phase to phase fault in the cables ahead of the motor, that would not immediately damage the motor and the OL relay should react in time to protect it (if allowed to). The issue, as stated many times now, it that the MCP prevents the SC or GF event in the CIRCUIT from causing a fire before other devices can react.
MPCB is a different animal, it is a THERMAL-Magnetic circuit breaker that has ADJUSTABLE thermal trips that can be set just like a bi-metal overliad relay. It IS the overload relay, in fact its UL listing is often that of a Manual Motor Starter. In countries outside of North America, adjustable thermal trips on circuit breakers are not unusual so there is no separate term for them. Here they were illegal in terms of calling them "Circuit Breakers" for a long time, because the concept of adjustable thermal trips was unacceptable for safety. So the only way to get them UL listed was as a Manual Motor Starter. More recently though, UL489, the standard for Circuit Breakers, was amended to include MPCBs, but for use ONLY on motor circuits. That's because UL508, which covers Manual Motor Starters, did not have the necessary testing requirements for interrupting capacity as UL489. So they added MPCBs to UL489 to require that added testing.
So there are now both versions available, different uses. Many people who do not build OEM motor control systems on a regular basis however are still unfamiliar with MPCBs yet because they are just now filtering down into the workplace.