Permeability is somewhat influenced by porosity but not always. Think of Swiss cheese, it has high porosity but very low permeability. Hydraulic conductivity is a property of the porous-fluid system together. It is a measure of the resistance to flow of a certain fluid through a certain porous medium. It is called the coefficient of permeability in Skinner and Porter.
Hydraulic conductivity is a more standard term.
Specific discharge is the volume flux of fluid which flows through a certain cross sectional area. Darcy's Law is a formula to calculate specific discharge through a porous media given that the hydraulic gradient and the hydraulic conductivity are known. To calculate the true velocity of the water particles you must divide the specific discharge by the porosity of the material. Aquifers An aquifer is a body of highly permeable rock lying in the zone of saturation. The total energy at a point in the aquifer.