Touge= Illegal Street Racing on Public Roads, Generally during the night (though not only at night), Usually two cars, one starts with a lead, generally the goal being to increase the lead for the front runner, or decrease it for the chaser, Drifting is an optional, but popular technique. It's much cooler to pass someone sideways, right?
Race Drifting=The way I drive my Rufs and Elises, just using small drifts to tighten my lines so I can overcook corners and let the rubber scrub excess speed off instead of the brakes, very risky, not very showy, but can be quite effective and fast, not to be confused with the next entry.
Exhibition Drifting=Throwing caution, and times to the wind, and focusing on getting as much angle, speed, smoke, and distance as you can in each drift, competitions can be judged on such things as linking corners, and doing Touge style "races" where one tries to not only close the gap/open the gap between cars, but also tries to outdo the other driver with showy drifts.