Is there any way to change what happens when I close the lid of my laptop?
Do macs have the option of hibernating vs. sleeping like PC's do?
If so, which of these is the default behavior when I close the lid?
macs do have hibernate and sleep, the default on newer machines is a combination. the closing of the lid saves to disk for hibernate but on wakeup if the battery has not run out it wakes from sleep. Macworld explanation
You can change it from the command line
sudo pmset -a hibernatemode 3
Or via preference pane
You can also leave the system to manage this automatically. It'll sleep, but hibernate in the background as it were, so it can wake quickly, but still survive a battery death.
Normally you'll find it was just asleep and waked immediately. If you the battery did die, then returning from hibernation you'll find the screen as you left it, but grey. It'll then load and colour up, until awake. Take only a minute.
The hibernation doesn't take that long, seconds anyway, and is the pause you see before the light starts breathing.