If the slope of the filter is infinitely steep, the filter has the same effect on every component below (or above) the cutoff frequency. Normally, acoustic filters do not have such sharp boundaries. The pass band refers to a part of the spectrum: sound energy in that frequency range is passed by the filter. The reject band refers to the other part of the spectrum: sound energy in that frequency range is blocked by the filter.
In common, the transition between pass band and reject band extends over some ranges of frequencies.