What is the difference between a “single-speed bike” and a “fixed-gear” bike? I would have thought that a single gear was the same as a fixed gear, but that does not seem the case.  What am I missing?

Can a fixed gear bike have more then one gear?
A single speed bike has a single speed freewheel threaded onto the rear hub. The freewheel allows the rider to coast.

A fixed gear has a single cog threaded on the rear hub, along with a reverse threaded lockring, to prevent the cog from getting loose. The cog has no freewheeling action, so any time the wheel is moving, the pedals are moving too. This setup allows the rider to even ride backwards.

Generally speaking, fixed gear bikes have only a single gear. There are some setups however where instead of a single gear at the rear a special dingle with two cogs is placed in, and a pair of chainrings is up front, and the tooth difference between the chainrings is the same as the tooth difference in the cogs. Then, the rider can change gears for different riding, however it requires dismounting, loosening the rear wheel, and manually moving the chain from one set of cogs to the other.

There are also some 3 speeds or other internally geared hubs that have been owner modified to be multi-speed fixed hubs, but they are very, very rare.