The fast stochastic plots raw %K and its average. The slow version plots the averaged %K as the main line and averages it again for the signal, which removes much of the jitter that makes the fast version unusable on noisy data.
This is the standard illustration of the smoothing trade-off. Each layer of averaging removes noise and adds delay; the signals are cleaner and later. There is no setting that gives you both.
Most platforms default to the slow version, which is why the stochastic most traders see is already double-smoothed. Knowing that matters when comparing settings across charting packages, because the same label can mean different calculations.
Related: stochastic-oscillator, indicator-lag, signal-line, stochastic-rsi, lookback-period