Temperature is a measure of how warm something is (at the atomic level how fast the atoms in the material are vibrating)

Power is a measure of work. The uni for power is watts which is equivalent to Joules/second. Basically it's a measure of how much energy the soldering iron can put into a material in a given time.

So if you have variable temperature then you have an iron that will reach a specific temperature but it may not be able to pass on the heat quick enough to the object if it is low powered and actually cool down.

If you have variable power, the iron will have that level of power delivered to it and reach some form of temperature equilibrium when the heat input to the iron is equal to the output to the environment.

To be honest all you need for robot work is 2 irons, one at around 25w for smaller jobs and one around the 100 to 150w mark for the bigger stuff. I got a 25w variable temperature one. Not for any other reason than my own perverse curiosity to know what temperature it's at. I use a big 150W one for the bigger jobs