Conductivity is the rate at which heat is conducted through a one inch thick layer of the material, in terms of Btu per hour per square foot of material per degree F temperature difference, or Btu-inch/h-ft²-F. Conductance is the conductivity for a given thickness of material, in Btu/h-ft²-F.
The U-value includes the conductance of every element of the building assembly, and including the surface conductance (air films) on the interior and exterior faces of the assembly. These surface conductance quantify the rate at which heat is transferred between the surface of the assembly and the surrounding environment. They contribute to the overall insulating qualities of a wall or roof in a significant way, and so cannot be ignored in energy calculations.