Yes, there is a massive difference, and you cannot invert them to get the other.

Watt per Intelligence means that you have a fixed, deterministic, measure of intelligence, and you calculate how many watts it takes to get there.

If your goal is to measure which model can reach a specific outcome with the least energy possible (which is what GP says the goal is for this metric), then you cannot have a variable outcome, which is what intelligence per watt describes. As opposed to watt per intelligence, where the outcome is fixed and the numerator defines how much energy expenditure is needed to reach this fixed outcome.