  Electromagnetically induced transparency (EIT) and Aulter-Townes splitting
(ATS) are two similar yet distinct phenomena that modify the transmission of a
weak probe field through an absorption medium in the presence of a coupling
field, featured in a variety of three-level atomic systems. In many
applications it is important to distinguish EIT from ATS splitting. We present
EIT and ATS spectra in a cold-atom three-level cascade system, involving the
35$S_{1/2}$ Rydberg state of cesium. The EIT linewidth, $\gamma_{EIT}$, defined
as the full width at half maximum (FWHM), and the ATS splitting,
$\gamma_{ATS}$, defined as the peak-to-peak distance between AT peak pairs, are
used to delineate the EIT and ATS regimes and to characterize the transition
between the regimes. In the cold-atom medium, in the weak-coupler (EIT) regime
$\gamma_{EIT}$ $\approx$ A + B($\Omega_{c}^2$ + $\Omega_{p}^2)/\Gamma_{eg}$,
where $\Omega_{c}$ and $\Omega_{p}$ are the coupler and probe Rabi frequencies,
$\Gamma_{eg}$ is the spontaneous decay rate of the intermediate 6P$_{3/2}$
level, and parameters $A$ and $B$ that depend on the laser linewidth. We
explore the transition into the strong-coupler (ATS) regime, which is
characterized by the linear relation $\gamma_{ATS}$ $\approx$ $\Omega_{c}$. The
experiments are in agreement with numerical solutions of the Master equation.
