This is related to the tradeoff between range, noise, and data resolution (i.e. precision).
According to the Dundee Satellite receiving station:
Bands 21 and 22 cover the same part of the spectrum but have different saturation points. Channel 21 saturates at about 500 K, and channel 22 saturates at about 335 K. Channel 22 is also less noisy.
Or, as formulated by the University of Hawaii:
Bands 21 and 22 both cover the same spectral interval but have different dynamic ranges; band 22 is sensitive to whole pixel temperatures of up to ∼330 K, band 21, ∼500 K. The band 22 detectors often saturate over highly radiant surfaces.
Imaging having a camera and imaging a scene with very dark and very bright spots. The dynamic range of a single photo will not capture the entire scene. So instead, you can take one photo with a very wide aperture, and one with very narrow; or you add a neutral density filter for one of the photos. By taking multiple photos, you capture a wider range of scene brightness, than you can with a single photo. This is broadly analogous.
(Thanks to uhoh comment for the amateur photography analogy.)
Or consider two classical expanding-liquid thermometers with the same size. One goes from 10°C to 35°C, the other from -80°C to +70°C. They're measuring exactly the same thing. The former will have lower measurement uncertainty within its range, and is more useful indoors (in a home or office). But unless you live in Addis Ababa or Mexico City, the other one may be more useful outdoors. The situation with the two seemingly identical bands is broadly comparable to this situation.