Not much of a difference. You just ensure that the results the algorithm produces look somewhat like what you might get from a much more complicated and accurate method. That's what real-time coding for games and/or the demoscene is based upon, after all, cheating. You've got 2 choices. 1) Show them one you made earlier and pretend you made it up on the spot, or 2) Show them one you knocked together on the spot that looks real if you squint, then make sure that they have to squint.
No no, with your approach it is a one-step process where the algorithm is applied, makes extreme changes, and it's done. That is "weathering" and it's not a simulation, it's a visual effect just like a ship skin. Some game engine devkits even have a Weathering slider they can use to make objects look older through an algorithm. They just drag it from left to right, the item changes, it's all done in one swipe. A simulation differs in that small variations early in the simulation can lead to huge differences later on.
If you take that Weathering slider in your typical FPS devkit and slide it back and forth you'll get the same results all day long. If you simulate the weathering effects you will get a different result every time depending on the random "seed" that was put into the algorithm in the beginning. Two entirely different processes are occurring, and only the latter is procedural generation.
Or you use a lot of approximation and false "detail" passes that make what you are generating appear/behave somewhat like you would expect from a simulation, but at a much lower cost in processing terms.
I'm guessing that most cloud generation is done with simple noise algorithms, not a full simulation of the water cycle. But if it appears to be cloud-like, does it matter?
Would you believe me if I told you this actually takes a lot more processing power than simulating weather effects? Approximating involves a lot of floating point calculations and computers don't like floating points. At least CPU's. GPU's, ASICs and FPGA's work well with floating points, which is why they're typically used in these applications, because you can take the shortcuts you are suggesting without it taking more time than doing it step by step. Moreover, this seems to be the exact opposite direction they are heading because if they had any intention of using floating point calculations heavily they would have converted the executable to 64-bit long ago.
I have a feeling Mr. Braben doesn't like shortcuts.