Pen tablets require minimal amounts of power. They get enough power from a normal USB 2.0 port.
Pen displays require much more power than a pen tablet due to the embedded display panel. They may have a power adapter that you need to plug into the wall. Or they may be able to be powered with through a USB-C cable.
Pen tablets that have wireless support have built-in batteries that can usually last the entire day and do recharge quickly when they are plugged back in.
Pen displays DO NOT have batteries. They must get their power from a cable that is either attached to a computer or to power coming from a wall.