  Extreme value statistics, or extreme statistics for short, refers to the
statistics that characterizes rare events of either unusually high or low
intensity: climate disasters like floods following extremely intense rains are
among the principal examples. Extreme statistics is also found in fluctuations
of global magnitudes in systems in thermal equilibrium, as well as in systems
far from equilibrium. A remarkable example in this last class is fluctuations
of injected power in confined turbulence. Here we report results in a confined
von K\'arm\'an swirling flow, produced by two counter-rotating stirrers, in
which quantities derived from the same global magnitude ---the rotation rate of
the stirrers--- can display both, extreme and Gaussian statistics. On the one
hand, we find that underlying the extreme statistics displayed by the global
shear of the flow, there is a nearly Gaussian process resembling a white noise,
corresponding to the action of the normal stresses exerted by the turbulent
flow, integrated on the flow-driving surfaces of the stirrers. On the other
hand, the magnitude displaying Gaussian statistics is the global rotation rate
of the fluid, which happens to be a realization of a 1D diffusion where the
variance of the angular increments $\theta(t+\Delta t) - \theta(t)$ scales as
$\Delta t^{\nu}$, while the power spectral density of the rotation rate follows
a $1/f^{\alpha}$ scaling law. These scaling exponents are found to be $\alpha
\approx 0.37$ and $\nu \approx 1.36$, which implies that this process can be
described as a 1D superdiffusion.
