As all the other replies have mentioned, it is the same thing if you assume linear dynamics and Gaussian noise in the KF. Besides non-linearity and non-Gaussianity, there are a few other extensions that make super useful - one is that you can add an external obervable/controllable control signal. Thinking of this as an "independent" variable that you can observe or manipulate to get your desired observed value of y. This will take you into the realm of control systems engineering. Also, it's trivial (computationally) to let the dynamics be a changing function of time (i.e. instead of the fixed matrix A, let it be A(t)) - this allows you to model some pretty sophisticated dynamical systems.