What do the numbers 1.2w and 1.8w on the water heater mean?

The 1.2w and 1.8w on the water heater respectively represent different powers. The larger the value, the greater the power, and vice versa.

Power refers to the amount of work done by an object in unit time, that is, power is a physical quantity that describes the speed of work. The amount of work is fixed, and the shorter the time, the greater the power value. The formula for finding power is power = work/time. Power is a physical quantity that represents the speed of work. The work done per unit time is called power, represented by P. Therefore, power is equal to the scalar product of the force and the velocity of the point on which the force is applied.