I would consider I=C dV/dt to be an equation which is derived from a special case of F(q,V)=0. In this sense F(q,V)=0 says it all and is the more general expression. For the case where F(q,V)=0 can be rearranged in the explicit form q=CV you obtain I=C dV/dt simply by taking the time derivative of q=CV when using the definition of current as I=dQ/dt and the additional assumption that the capacitance C is constant.

We can draw q-v characteristic, but we cannot draw i-v characteristic beacuse it depends on current (or voltage) waveform. So, according to this property i-v characteristic and i=Cdv/dt should not be the constitutive relation. Am I wrong?