I don't know the German terms for either of these, but perhaps a description would help.
In a car, play is what the steering wheel has on an older car. It's the distance you can turn the steering wheel before the wheels of the car actually change direction. It happens when the steering gets looser over time. New cars, and especially sportier models, have very tight steering, so that the slightest movement of the steering wheel is reflected in the path of the car. Older cars, and especially large unsporty American family sedans, have much more room for error in steering; that is, you have to turn the steering wheel much farther, more decisively, to make the car actually change direction. So the steering (wheel) has more play.
Clearance, in contrast, is the distance between a moving part and something that could impede its movement if it got too close. In a car, for example, you might speak of the clearance between the driver's head and the interior roof of the car. Or the wheels of the car might need a certain amount of clearance to be sure the tires don't rub against any other body part like the fenders. Another typical use of clearance is the space necessary for a truck to pass under a bridge or overpass; it's usually marked with a sign.
So play is the distance a loose moving part (attached at one point) can travel (away from that point) without seriously affecting its function/operation. But clearance is the empty space between a moving part and a fixed obstacle that's necessary to prevent the former from hitting the latter.
Does that help?