I'm going to take a stab at this, assuming that the eVic wattage mode would be the same as other temperature controlled devices' wattage mode. In regards to the other stuff, I am sure someone else will correct me if I'm wrong in regards to application to the eVic or other details. Hopefully I am not going on this rant and misreading the question lol.
Wattage mode would be used with non-temperature control friendly atomizer
coils, such as those made out of kanthal or nichrome. In this mode, your device is applying the wattage that you set consistently and as long as you press the fire button. The risk with this is that you can dry hits or burnt hits because the temperature is not being regulated and whatever wattage you have set is constantly being applied.
In temperature control mode, your eVic is applying wattage up to the temperature that you have set and then regulating the wattage to maintain/be around that set temperature. The device can "read" the temperature of your coil as it is constantly monitoring the resistance of the coil/atomizer. Because metals like nickel and titanium have a known temperature coefficient of resistance, the device can "estimate" at what temperature your coil is at based on the resistance of the coil the chip or board in the eVic is sensing. Kanthal and nichrome don't have a predictable change in temperature based on change in resistance like nickel or titanium does and so they cannot be used with temperature control mode (although to be technical it seems as though nichrome has a TCR, but is too low to be utilized by the devices/chips currently on the market).
If you have the eVic kit, you likely have titanium and nickel
coils, and these are currently the most common atomizer coil materials used with temperature control devices and temperature control mode. It is best to run these
coils only in temperature control mode as that is how they operate best and most safely.