Could someone please explain to me the relationship between frequency bands and channels?
The answer is mostly political: spectrum allocation is handled by the regional authorities based on a large number of economical, technical, political factors, and not the least on how much money can me made selling or leasing the rights. In the US that's done by the FCC.

This being said, most bands tend to have constant relative bandwidth, not absolute bandwidth. Bands that are centered in the GHz range are typically 100s of MHz wide. Bands that are centered in the 100kHZ range are maybe 10s of kHZ wide (if at all).

Using this reasoning you would expect 5 GHz band to have roughly twice the bandwidths than the 2.4 GHz band. Since the WIFI channels are constant absolute bandwidth (20 MHz), there will be more channels the higher the center frequency of the band is. But again, it's most regulatory determined.