The K3 and thus presumably the K3S implements one particular form of the Least Mean Squares algorithm called the Leaky LMS, see Lyle's response some years ago:
http://elecraft.365791.n2.nabble.com/K3-NR-td1557606.html#a1557836That's an adaptive version of a Wiener filter that doesn't get so easily 'stuck' in a non-optimal solution if signal statistics should change drastically. Instead the non-optimal solution 'leaks' out of the filter.
The Wiener filter by itself is a fixed signal-to-noise optimizing filter, and thus is fundamentally different from low pass, high pass etc in that the filter's coefficients depend on the input signal.