Is the critical frequency the same as the MUF?
The critical frequency is the highest frequency which will be reflected when the radio waves are directed straight up. Frequencies higher than this are not reflected, but continue into space.
The critical frequency is essentially the MUF for the case where the transmitter and receiver locations are the same - where the radio waves go straight up and get reflected straight down. As you move further away from the transmitter site, the MUF goes up, as the incidence angle of the radio waves becomes more shallow. Eventually the angle is such that the waves will be reflected back to Earth. This is the cause of the "skip zone" around a transmitter site, where a signal cannot be heard. The frequency is too high to be reflected back to Earth at that angle. Further away from the transmitter site, it can be received.