All digital filter frequency parameters (passband begin frequency, passband end frequency, and stopband begin frequency) are stated in terms of an input signal sequence's Fs sampling frequency. For a lowpass filter example, if I said a lowpass filter's passband width (it's "cutoff" frequency) is 0.2, I'm saying that the cutoff frequency is 0.2 times Fs. So if an input signal's Fs was 1.0 kHz that lowpass filter's cutoff frequency is 200 Hz. However, if an input signal's Fs was 20 kHz then in this situation that same lowpass filter's cutoff frequency is 4 kHz.
For a different scenario, if you said, “Rick, please use Matlab and design a digital lowpass filter whose cutoff frequency is 300 Hz.” It would be impossible for me to do that unless you told me what was the filter’s input sequence’s Fs sample rate. But if you then said “Fs = 1000 Hz”, then I’d know the filter’s ‘normalized’ cutoff freq was 300/1000 = 0.3 enabling me to design the lowpass digital filter.