This study presents 2D simulations of the two-chamber inductively coupled plasma source where power is supplied in the small discharge chamber and extends by electron thermal conductivity mechanism to the big diffusion chamber. Depending on pressure, two main scenarios of plasma density and its spatial distribution behavior were identified. One case is characterized by the localization of plasma in the small driver chamber where power is deposed. Another case describes when the diffusion chamber becomes the main source of plasma with maximum of the electron density. The differences in spatial distribution are caused by local or non-local behavior of electron energy transport in the discharge volume due to different characteristic scale of heat transfer with electronic conductivity.