Units for flux density

While I do understand the use for the displacement vector D = (e0)E + P, I don't quite understand why they label it as "flux density". The units for the displacement vector are C/m^2. The units for electric flux are Vm, so wouldn't electric flux density become Vm/m^2 = V/m which is just equal to the electric field?

edit: C/m^2 just looks like surface charge density...