I think it refers to mainly aquifers but some times in both the situation . There are number of variables and parameters which are implemented in view of the groundwater level.Soil moisture content, hydraulic diffusivity and movement through Z direction.

i think that hydraulic conductivity is a function of two parameter, first is the soil significant diameter of its particles (permeability) and the other is the water characteristics of specific weight and viscosity, so it refer to the aquifer ability to transmit water and may be affected by the soil water content  

Hydraulic conductivity (K) is a generic term that describes the ease with which a fluid/water moves through pore spaces/fractures.  K is a property of soils, rocks as well as vascular plants, and could be applied to both aquifers and vadoze zone.

The permeability of saturated medium is different (generally higher) compared to the permeability of the unsaturated medium (lower, because of the air that has a very important role). Even the calculation of the permeability is different. In any case, there is an extensive knowledge of this subject and a lot of Authors studied the unsaturated zone (e.g.  Van Genuchten M.T., Green R.E. etc.).

Hydraulic conductivity is a function of the rock properties (permeability) and fluid properties (fluid density and dynamic viscosity). Saturated hydraulic conductivity (Ks) is the an aquifer parameters which is constant while unsaturated hydraulic conductivity k(f) is function of the negative pressure head of the unsaturated zone (which is a function of soil moisture content). Both saturated and unsaturated hydraulic conductivity have major impact on the infiltration and recharge rates

The ability of porous media for conducting flow, is defined by hydraulic conductivity. It is a general definition for porous media and so, is applicable for groundwater. Hydraulic conductivity depends on characteristics of porous media (porosity, saturation percent , ...) and fluid characteristics( viscosity, density, ...).

As noted above, hydraulic conductivity (K) is the ability of the porous medium to transmit water, which becomes limited if air partially fills the pore space. If the pores are completely filled with water, K is the saturated K, which is the max for the medium. As the amount of air filling the pores increases (and the water filling the pores decreases), the pores become partially blocked by the air, which decreases the K.

The hydraulic conductivity of the vadose zone is highly variable with depth and is represented by the hydraulic conductivity curves plotted as a function of the pore water capillary pressure (or succion).

Well,

more details found in 16 chapters,/ by Tindall et al, 1999.

Sincerely

This article can help.