Comparing A* search to Simulated Annealing
"Energy" is just the output of your cost function that you define for the SA problem. You are right that the two algorithms seem to have two different purposes, and in most cases, I would say that is true. However, you could pose a pathfinding problem as a simulated annealing problem, depending on how you define your cost (energy) function.

Let's say you have a cost function that equals the total cost to get from point A to point B. Your SA algorithm would try to find the minimum in this cost function, but imagine how difficult that may be. Your cost surface could potentially by many-dimensional. Plus, there is no guarantee that your cost surface is smooth, so finding that minimum on this enormous cost surface may be computationally intractable.

I think you've stated well many of the differences, but the next step is to try to understand the benefits/drawbacks of each algorithm solving the problem they are best suited for.