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An "overdrive" is not always an extra gear. In fact, I believe that most of the time nowadays an "overdrive" is simply a transmission gear that is "taller" than 1:1. The 1:1 drives are sometimes called "direct drive" because some designs would have the input and output shafts in line with each other, and the "direct drive" gear would physically lock the two together without pushing the power through the gears. This was more efficient than going through the gears, though you still lost a little bit to spinning the other parts in the transmission.
There was a while where cars had external "overdrive" units between the transmission and the differential. Those were basically mini two-speed gearboxes that would let you select "high" or "low", changing the effective gear ratio. But I can't think of any new cars that have had those in several decades.
Some automatics would call their top gear "O/D", and you could lock it out if you needed engine braking, such as when going down hill. I remember a few (rental) cars that had a button to enable or disable the O/D gear...
But chances are in this case that "overdrive" simply describes a somewhat tall top gear.
-soD
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