Interpretation of the photon scattering rate?

The photon scattering rate $Gamma$ describes the rate at which photons scatter off an atom$^1$. In a two-level system, the ansatz for the photon scattering rate often is given by

begin{equation}
Gamma = rho_{22}gamma
end{equation}

where $rho_{22}$ is the probability to find the atom in the excited state and $gamma$ is the rate of spontaneous decay. However, I don’t see the connection between the ansatz above and what the photon scattering rate is physically meant to be.

$^1$In my imagination, the photon scattering rate is the absorption rate for photons at a certain frequency $omega$. Hence $Gamma(omega)$ shows the saturation broadened Lorentzian absorption line of the atom, centered around a resonance frequency.