What is "the conductivity we usually use"use”?
You apply an electric field E$E$ to a solid and get a current j=\sigma E$j = \sigma E$. The proportionality coefficient \sigma$\sigma$ is the conductivity.
If you apply a time-independent electric field, the conductivity \sigma$\sigma$ is a just a number and is the static conductivity of the medium. If you apply a time-dependent electric field, e.g. E(t)=E_0\cos(\omega t)$E \left( t \right) = E_{0} \cos \left( \omega t \right)$, the conductivity \sigma(\omega)$\sigma \left( \omega \right)$ becomes a function of the frequency \omega$\omega$ and is the dynamic conductivity of the medium.
The static conductivity \sigma(\omega=0)$\sigma \left( \omega = 0 \right)$ is a special case of the dynamic conductivity. The static conductivity of a dielectric is zero. The dynamic conductivity of any medium, including dielectrics, is always finite. The
The sentence "ac conductivity might be considered a form of impedance spectroscopy" in the previous answer ifis meaningless, since the conductivity is a physical quantity which characterizes a medium, while any spectroscopy is an experimental method to measure some physical properties of a medium, e.g. the dynamic conductivity.
