interesting. sounds like some kind of bad initialization in the code (i.e. likely in the addon not your code), if it's returning different fits each time.
3rd order = using terms in x^3, x^2, x, y^3, y^2, y and combinations of these
4th order = using terms in x^4, x^3, x^2, x, y^4, y^3, y^2, y and combinations of these
(i.e. it doesn't change the dimensionality of the inputs or outputs, but changes how complex the model is which goes between the inputs and outputs)
if you just call fit multiple times in the same session what happens?