Xboxone s controller?

I have an xbox one and an xbox one s at home. However, the controllers of the xbox one are no longer as good, but there are games on them that are not on the xbox one s. My question is can I connect the xbox one s controller to the xbox one, although both consoles are within range of the controller and if so, how?

Yes, but you can only connect a controller to a console at the same time.

Yes, of course you can connect the controller to another One.