The list of events shows different power values? Is this normal?
Generally the On and Off values will be the same, but in some cases they can show different values. Cold lamps will drain more current than lamps that are already hot. So when you turn them off, they already drain less current, thus less power.
A fridge for instance, has an electric motor to drive the compressor. When the motor starts, from a standstill position, it will drain more power (thus current) during a fraction of a second, until the cooling fluid is circulating. So let's assume that your fridge, when starting to cool, uses 45 Watts of Power. After a typical period of 5, 10, .. minutes, your fridge will have reached the 4°C set point and the motor will stop cooling. The total power measured in your home (being the total of all your appliances at that specific point in time), will then suddenly be reduced as your fridge just stopped cooling. You would expect a reduction of 45 W (same as the initial power when starting), but in practice you will notice a reduction of a lower power, e.g. 40 W (as once the motor is running, it drains less power). Smappee will match those power changes with statistical methods (e.g. I see a +45W, then a -40W, again +45W then a -40W, etc.) Of course it is more difficult than this, as ten's of other equipments turn on and off in the meantime. Or certain device of e.g. 2000 W vary easily with 40W when draining their power. So the difficulty is to match the power changes to the right appliance. Many other difficulties include things like dimmers ( power goes from e.g. 10W to 250W for the dimmed light), LED TV's (depending on the movie you watch, power of the LED varies a lot!), ..