The expression 'overdrive' has been used for this type of gearbox ever since it was first introduced, even in Germany. It describes a situation which goes over and above the 'normal' operation. Perhaps one could also say, that an additional two-speed gearbox has been added.
Originally the expression comes from Great Britain, where in bygone days, the heavy taxes imposed by the government on the cylinder-bore, caused a flood of long-stroke engines. The advantage of better torque faced the disadvantages of smaller valves and higher piston speeds.
This is exactly the solution offered by the overdrive. It is engaged in third- or even more sensibly, in fourth gear, and changes the gear-ratio to allow higher speeds at lower revs, thus putting less strain on the engine.
Such a low-ratio, top gear is nowadays, also called a cruising gear, although overdrives have not been around for a long time anymore and their
function has been integrated into the normal gearboxes. At the time of it's introduction, the overdrive was an optional extra, it could also partialy be substituted for by a longer drive-shaft and a different gear-ratio.
In the beginning, the overdrive had it's own separate gear-lever (see picture), afterwards it could also be engaged by pressing a button, whereby, individual gears (e.g., 1st and 2nd) could be blocked out. Of course, such a cruising gear has a positive affect on the noise development and the consumption, indeed, the acceleration is not quite as fast.
In this case, we are mostly, but not always, dealing with a planetary gearbox. A manual gearbox with overdrive, makes it possible, through the axle-drive, to achieve a ratio of 1 when driving in the mostly used, top gear, which also maximises the efficiency. 03/13