I am sorry, but you are possibly misled. All e-bikes have three major components. A Battery (stored energy), a motor (which converts electrical energy to mechanical motion at some given rate), and a controller (which meters out the energy to the motor under user and factory set parameters, maintains the Li-Ion batteries within safe limits, and monitors motor and battery temperatures).
The battery Wh rating does NOT control speed at all but does affect how far the bike will go at whatever speed the motor will maintain. The Wh rating is a measure of the total stored energy. Think of it as the "size" of a water tank. A larger tank will hold more water. The "Watt" rating of the motor gives a better indication of the power of the motor, and thus the "rate" at which water can be drained from the tank. A 500W motor represents a bigger drain than a 250W motor, but the 691Wh tank is still the same size. The voltage (36V vs. 48V) does have an indirect affect on speed in that for a given DC motor, it will run faster at a higher voltage. Think of a 48V batter as able to exert more "pressure" than a 36V battery. Thus a 324 Wh @ 48V battery (6.75 Amp) might deliver more energy over a much shorter period of time than a 691 Wh @ 36V (19.2 Amp) battery can.
In the case of most of our bicycles, they are regulated to specific top speeds by the controller. The Specialized Turbo (all models) are limited to either 25 kph or 45 kph based on country specific regulations. The Turbo S (500W motor) can get to 45 kph faster than the regular Turbo (200W motor) but they both top out around 45 kph. You are correct in stating that the battery controls the top speed of the Specialized bikes in that the controller that limits this (25 kph vs. 45 kph) is in the battery firmware and can only be changed using the dealer diagnostic.
The Akku bike (I assume is not Specialized) may have entirely different controls. The settings for its top speed (or lack thereof) could be in the motor or in the controller or in the batter.
