I noticed a long time ago that sometimes a reboot wouldn't set things right by itself, but a full shutdown followed by an ordinary statup would. That was at a time when things like audio cards, video cards, and network cards were separate things that were plugged into a motherboard, not just chipsets. Rebooting the OS didn't necessarily cut power to those accessories and cause them to re-initialize.
The most common example back in the day was a network card that got confused for some reason, and stayed confused after a reboot, but worked fine once the computer was turned off and then restarted.
Depending on a computer's architecture, that may still be true today. I've formed a habit such that if a single reboot doesn't cure a problem that I expected it to, I'll do a full shutdown and restart. I can't remember a time when that hasn't worked for me.
