Yes, there is a difference between shutting your computer down-also called a cold boot-and just restarting your computer. Restarting, as far as I have found out, really doesn't shut down the computer, but let's the computer add new information if you are installing a new program or something like that. Shutting off your computer for any length of time is usually for making hardware changes or working on the pc, etc. Sometimes I turn mine off for the night, other times I leave it on.

Usually, when installing programs, the install setup will tell you either to restart the pc or shut it off for a few seconds. It's important to do what the program says. Otherwise programs won't get installed properly.