Easy part first - if you run shutdown your computer ends up being off. As in no power. As in, very difficult to fix remotely :). Reboot restarts everything.
It is fairly rare to require a reboot under linux - the only reason to reboot that I can think of is if you upgraded the kernel, if your machine is crashing really badly, or if you want to install some types of new hardware (RAM, plug-in cards etc).
Mostly, when you edit "important files in /etc", you can restart just a part of the system. For example, you might need to restart just your webserver.
There is no complete rule. Try googling "reload ". For example, googling "reload /etc/security/limits" suggests logging out, then logging back in.