This may sound dumb, but I haven't heard much about this. What's the difference between sleep and shutdown? How do you do each?

Sleep, or standby (when you put the case on the front side), is like sleep on a laptop. It stops most the actions, but it still draws power from the battery or plug.

Shutdown, done with the power button, or issuing a shutdown command via the command line. Is like shutting down a pc. It saves everything it's been working on, and then powers off. While you'll get some discharge leak from a battery over time, it will last a lot longer than if it was in sleep.

interesting, i never knew about the sleep function. does it kill the internet connection and applications using network?

It doesn't stop the apps, but it does drop the wifi. I don't have a bluetooth phone so I can't test that, but I'm assuming it would because sleep is meant as a standby, to save battery life. If you look at the docs Nokia says 3 hours on wireless, more if you go into offline mode (from other users), and in standby / sleep the battery will last about 7 days.