What is the difference between the chemical potential μ and the molar Gibbs free energy Gm?
The chemical potential of a species is the partial derivative of the Gibbs free energy of the mixture of components with respect to the number of moles of that particular species, holding the temperature, pressure, and number of moles of all the other species constant.  For a single component system, this is reduces to the total free energy divided by the number of moles.