The DS touchscreen is a pressure-sensitive screen. You can use the stylus, your finger, a lightsaber, end of a paintbrush, anything. So long as the tip of whatever you use creates a certain amount of pressure on the screen surface to make contact with the screen itself, you can use the touchscreen.
The DS touchscreen has a transparent film that separates it from the screen. The DS stylus creates a connection with the screen via pressure on that outer layer against the screen and the DS translates it as contact. You need to press pretty hard with your finger to get the touchscreen to register, but the stylus is made to make that connection with minimal pressure.
Tablet touchscreens are capacitive screens. An electrical current runs along the underside. Your fingers and a proper capacitive stylus (rubber tip) will interrupt that current and the screen translates it as a contact point. This configuration allows for multiple actions on the screen, such as "zooming" by spreading your fingers.
The DS stylus is not a capacitive stylus and a capacitive touchscreen will not register it, as it is incapable of interrupting the current.
The more you know...