You're probably coming from BB like I did where the normal shutdown pretty much just puts it in standby. I don't think that is the case with the Droid. If you do the power off, as stated above, it will do a full power cycle.
Battery pulls are not necessary with the Droid. At least not on a regular basis.
It's not a bad idea to reboot once in a while. Kind of cleans things up. You may also want to get the Cache Cleaner app in the market. It does everything one at a time but at least it works.
If the phone is powered off, it is powered off. Hold the power button till the menu appears
Standby is the screen timing out or you hitting the screen lock button and the phone going dark. And then being able to hit the lock button again the phone wakes up