I don't see how you got there. Numerical analysis is a whole branch of computer science which regularly deals with slight differences in computation. The usage of a constant (like pi) that is one bit different could cascade into massive differences in the results between the two programs.

Neither are completely wrong (as their results are similar) they just aren't exactly the same, especially when dealing with 7 day forecasts, this isn't to be entirely unexpected. We are trying to approximate massive systems we don't fully understand. A physics simulator is decent at getting a broad sense of things, but is not precise enough to get it exactly right, even though we use them to fly airplanes, same thing here.