There are some differences when dealing with digital control versus an analog control. Digital control is different than analog control in one large way. Digital is about discreet points, ones and zeros, so there is an affect called quantization, that appears in the ADC  resolution, PID compensator bit width, and in the digital PWM generator resolution. There are also delays in the ADC conversion and processing through the compensator and digital PWM. However, there are delays in an analog system as well. For instance, the PWM modulator would have a delay associated with it, and all of these are seen as phase delays in the system.