The iPad never sleeps (really)

From emperical evidence, I have established that the "sleep button" on the iPad does not actually put the device to sleep, but merely turns off the screen. Possibly this is also true for other iOS devices.

Item one: if an iPad is paired with a bluetooth keyboard, another iPad/iPhone can't use that keyboard, even if the first iPad is "asleep"!

Item two: if an app, say just a clock app, is running when you hit the "sleep button", the battery drains much faster than if no app had been running.

Item three: an app which had been running when you put the iPad "to sleep"  does not boot up when you press the "sleep button" again, it merely is still running, and since we don't yet have iOS 4.2 with multitasking for iPad, this can only mean it's been running the whole time.

Item four: the iPod app keeps playing on the iPad after the device "goes to sleep". 

See illustration, they call it "sleep", not "screen off".

I think this is very odd, and I don't know why Apple has chosen to do it this way and to call the button something it is not. But it's good to know it, so you'll know to save battery power by leaving nothing running when turning off the screen. And if it's critical, perhaps turn off the device altogether (hold down the sleep button). It might have security repercussions as well.