What is the relationship between Lion's Resume feature and Safe Sleep?

I have disabled the "Restore windows when quitting and re-opening apps" checkbox in the General preferences pane in Lion, but after a recent sudden power loss (no battery) my iMac restarted in exactly the same state as I had left it the night before. What feature of Lion is making this (miracle) possible, and how do I ensure that it remans enabled? --- I read for example that I can "disable Resume", because it "duplicates" something called "Safe Sleep", but I'm not sure what any of these features are, how they are related, or how I can control them. For example, does the behavior I saw in my recent power loss mean that my machine had gone to sleep between my last use and the power failure, or is some kind of snapshotting taking place continuously in the background? I also understand that there are different "kinds " of sleep. If sleep is indeed necessary, do different triggers (keyboard, script, idle, etc.) for sleep result in different "kinds" of sleep.