Hi,
I needed to quit an app,
because it gave me some problems (today).

Mostly (always in my case) an app** which behaves naughtily (= doesn't behave as it should), cannot be terminated in the dock, because it does not even show up there. (The dock is the lowermost area on the iPad).

(** today the app was DropCopy)
....

Now then I thought I had to restart the iPad as described here:

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Restarting the iPad:
Press and hold the Sleep/Wake button for a few seconds until
the red "slide to power off" slider appears, and then slide the slider.
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But this is only some kind of "sleep" for the iPad,
so the QUESTION is:

How to restart the iPad, so that all apps have to restart as well?

(Should it be done this way:
(Reset your device only if it is no longer responding and the steps above do not work.

(Press and hold the Sleep/Wake button and the Home button together for at least ten seconds, until the Apple logo appears.)

.................................................. ......................................
bw, Omar K N

Your second scenario is correct. If you slide the "power off" slider, it will "power off" (not sleep) the iPad but it will not reboot it.

To quit an app without rebooting, double press the home button, and in the multitasking bar that pops up press and hold an app until it jiggles. Then tap the red circle in the top left to completely quit it. Do this for all apps down in the multitasking bar and you won't have to reboot.