One way to look at it is that phase shift is in reference to a fixed frequency. PWM may or may not hold a fixed frequency. Others will no doubt have other explanations.
PWM power supplies vary the duty-cycle of a fast switch connected to the rectified DC to control the output voltage efficiently.
SCR supplies vary the phase shift of the SCR firing point with respect to the AC waveform. The SCRs are part of the AC input rectifier bridge to control the DC output voltage. Generally with this scheme you need to add some type of linear regulator to provide a low noise output.