Controller: in order to play with a controller you must use buttons, joysticks, and have to be connected to a console in order to operate it.
Touch screen: using a touch screen tablet is different because there are no additional buttons or joysticks to operate, and you're not required to be connected to a console.
Overall, controllers have more external parts while tablets/touch screens are flat with everything built into the screen. Another point is that you operate both items differently. Such as, a tablet requires the touch of your skin to sense you, but you could use a controller with gloves on.
