I'm not sure about "Require Passcode Immediately". Mine is checked for "Immediately" but my screen lock is set for a time and that time holds; it is not overridden by "Immediately". It may refer to when the passcode is required to unlock the iDevice.
Hmm, that might make sense. For example, screen goes to sleep and is dark after 15 minutes. When do you need to enter the passcode to unlock it? "Immediately" is just that—once the screen goes black you need the passcode, immediately. If instead of "Immediately" you had checked "5 Minutes", any time in the first 5 minutes after going dark you could just wake up your iDevice without the passcode. After 5 minutes you need the passcode.
So the Auto-Lock setting determines when, after a set time of inactivity, the screen will go dark. The "Require Passcode" determines how much time you have after dark to unlock the iDevice without the passcode. I have not tested this by changing various times in the two settings, but it seems reasonable.