  The nature of charge degrees-of-freedom distinguishes scenarios for
interpreting the character of a second order magnetic transition at zero
temperature, that is, a magnetic quantum critical point (QCP). Heavy-fermion
systems are prototypes of this paradigm, and in those, the relevant question is
where, relative to a magnetic QCP, does the Kondo effect delocalize their
$f$-electron degrees-of-freedom. Herein, we use pressure-dependent Hall
measurements to identify a finite-temperature scale $E_\text{loc}$ that signals
a crossover from $f$-localized to $f$-delocalized character. As a function of
pressure, $E_\text{loc}(P)$ extrapolates smoothly to zero temperature at the
antiferromagnetic QCP of CeRhIn$_5$ where its Fermi surface reconstructs,
hallmarks of Kondo-breakdown criticality that generates critical magnetic and
charge fluctuations. In 4.4% Sn-doped CeRhIn$_5$, however, $E_\text{loc}(P)$
extrapolates into its magnetically ordered phase and is decoupled from the
pressure-induced magnetic QCP, which implies a spin-density-wave (SDW) type of
criticality that produces only critical fluctuations of the SDW order
parameter. Our results demonstrate the importance of experimentally determining
$E_\text{loc}$ to characterize quantum criticality and the associated
consequences for understanding the pairing mechanism of superconductivity that
reaches a maximum $T_\text{c}$ in both materials at their respective magnetic
QCP.
