Using those settings on the Stockcharts "slow stochastic", the current values for %K and %D are:
Stockcharts: 36.14 and 36.51
AskResearch: 37.53 and 41.60
For the Stockcharts "fast stochastic", that produces a %K and %D of 27.7 and 34.3.
I think the Stockcharts version must use a curve-smoothing constant like in the ema calculation, and that this constant is different for the "fast" and "slow" stochastic.