The transmission case houses the gears responsible for changing the speed and torque ratios, allowing the engine to operate efficiently across a range of speeds. The final drive is often a separate housing, especially in vehicles like motorcycles, bicycles, and some cars (especially those with rear-wheel drive). This final drive contains the final gear reduction which changes the rotational speed from the output of the transmission to the drive wheels.
Therefore, the exact container depends on the specific vehicle and design, but it generally involves these two housings working together.