Lubricants used for gearboxs (manual or automatic) and the rear differential in your vehicle are different from those used for the engine. Transmission Lubricants have a life much more important. They must last 120000 miles for a truck or even the lifetime of the vehicle for some models such as Mercedes-Benz. Transmission lubricant must be chosen in accordance with the recommendation of the manufacturer of your vehicle.
The viscosity defines the resistance to fluid flow. For a lubricant varies with temperature. The choice of the viscosity of oil will therefore depend on its use (engine, transmission, hydraulic,...)