I'm just trying to figure out the difference between permanently identifying the drive with a static unchanging letter that is the same anywhere I plug the drive in and saying "yes, give me a letter when I mount this drive... any letter will do."
To be clear, the drive letter is not stored on the drive. The drive (partition) has a serial number that is stored on the drive when windows formats the drive. What you are doing when you assign a drive letter in disk management is to tell windows that when it sees the drive with that particular serial number it should assign that particular drive letter to it. That link between the drive serial number and the drive letter is stored in the windows installation on that computer. So if you assign a static letter, then disconnect the drive, and reconnect it to the same computer (but not necessarily by the same USB socket) it should still appear with the same drive letter. But if you attach that drive to another computer, it will not have the same drive letter it had on the first computer except by accident.
If you do not assign a static drive letter in Windows to a drive, then windows will assign a new drive letter every time it is attached. That might turn out to be the same letter, or it might not depending on whether you have other drives attached in the mean time. For programs that depend on accessing a drive at a certain letter, temporary drive assignments are a pain. You have 26 drive letters, and probably you do not have 26 drives/partitions, so you have a lot of flexibility. It does not make sense to assign a static letter to every flash drive you might plug in, but if you use an external hard drive for backing up the computer for example, you can set your backup program to automatically send backups to that drive by setting a static letter. You can use the same drive to backup another computer, using a different drive letter on that other computer by setting the same drive to two different static letters on the two different computers.