A frequency band was a specific range of frequencies from low to high; where the bandwidth was the width of said band.
While stranded on the surface of Ekos in 2268, Spock a modified communicator, which was said to lack its original range, to contact the USS Enterprise. When read by Uhura aboard the ship, it was said to be "nine points into the low-frequency band". (TOS: "Patterns of Force")
During the USS Enterprise-D second encounter with the Borg, in 2366, analysis of the conflict determined that after Data started to fluctuate the ship's phaser resonance frequencies, the Borg cube's tractor beam released the ship once the phaser frequency spread was in a high narrow band. With that information, he conceived that the cube's power distribution nodes were also vulnerable to those frequencies. Geordi La Forge considered that if the Enterprise could generate a concentrated burst of power at that same frequency distribution, they might be able to disable the Borg ship. However, the only means this could be attained was through the ship's main deflector dish. (TNG: "The Best of Both Worlds")