A simpler explanation for the use of channel numbers for TV and frequencies for FM and AM radio is that (1) AM radio operated in a contiguous band covered by an analog variable tuning capacitor and never had separate channel numbers, so (2) people were used to tuning in radio stations by frequency on a dial, and (3) FM radio likewise was in a contiguous band covered by a an analog variable tuning capacitor, so people were comfortable tuning in the station by frequency.
Television, on tho other hand, started out in two discontiguous VHF bands, with somewhat variable spacing between channels and a need for precise tuning, and tuning in on a single band by twiddling an analog variable tuning capacitor to the right frequency would have been difficult. This tuning method was used on some early TVs; I don't know whether they were tuned by numeric frequency or by channel number, but it would not have been very convenient. The TV industry instead standardized on TV tuners that had 12 discrete fixed settings, pre-tuned to channels 2-13, with a fine tuning control that allowed one to tune the frequency higher or lower to account for offsets. Later on, tuners had separate fine-tuners for each channel so one wouldn't need to retune when switching from station to station. Given the move to fixed- position tuning, the use of "digital" numbering of channels instead of analog-like frequency designations was an obvious simplification.
When UHF was added, it used a single contiguous band, and most sets initially required a separate converter box, which had an analog-style variable tuning capacitor that required careful attention to get the station one wanted (the pointer is between 30 and 40, is that channel 33 or 36?), but the tradition of using channel numbers instead of frequencies prevailed due to the established TV tradition. Eventually, TVs incorporated the analog-style continuously variable UHF tuner and later adopted a fixed-position tuner for UHF. Modern technologies, including Phase Locked Loop tuning and digital input and display, have relegated the dual-dial tuner and the fine tuning control to the dustbin of history.
Michael D. Sullivan Bethesda, MD, USA Replace "example.invalid" with ".com".[TELECOM Digest Editor's Note: This is true, however if you look at some FCC documents on FM radio frequency allocations (for example, documents on which frequencies are available on which places for 'low power' FM). All those documents show both 'frequency' and 'channel number' for the spaces between 87.6 FM and 108.1 FM. I think they have the 'channels' beginning at 201 and numbering upward. PAT]