The difference lies in the underlying mathematics. The free-energy surface (FES) is the Boltzmann weighted PES. Therefore, you require knowledge of the converged PES to plot the FES. The PES and FES do not always have the same characteristics, and so in the field of biophysics, it is customary to show the FES, while in fields such as reaction dynamics, the PES is most commonly used.

My understanding is that a potential energy surface does not take into account, kinetic energy effects and other bulk properties. But that depends on which of the Free Energies you are talking about. My sense of it says that if for instance you are looking at a G = H - T*S (Gibbs free energy) surface, you are incorporating entropy/temperature effects (Boltzman distributions), as well as pressure (H = U + P*V). If you look at a potential energy surface instead, you are going to ignore most of those terms, and also leave out kinetic energy contributions, since U = Total E = Kinetic + Potential. I guess different folks focus on different things. Creating the corresponding surface would involved using the appropriate mathematical relations. Please check me on that.

Free energy FE is energy that is capable of doing work. Potential energy PE is energy corresponding to position relative to a given datum. A simple example of the distinction: The PE in Earth's gravitational field g of a molecule of mass m in Earth's atmosphere at altitude z above a sea-level datum is mgz (z assumed much smaller than Earth's radius). If the atmosphere were isothermal, at thermodynamic equilibrium at temperature T, the probability density of a molecule being at altitude z would be Boltzmann, proportional to exp(-mgz/kT). The molecule's average PE would be = mg = mg(kT/mg) = kT. But its free energy FE = [T times (Smax - S)] would be ZERO, because total entropy S is maximized at Smax. Entropy is delocalization. The Boltzmann distribution is the best possible "compromise" between maximizing delocalization in position space of the molecule plus delocalization in momentum space of its heat bath. The heat bath would be maximally delocalized in momentum space if the molecule's altitude were fixed at z = 0. If the molecule is freed to move upwards it becomes more delocalized in position space, but because this costs energy from the heat bath, the heat bath becomes more localized in momentum space. Delocalization of the molecule in position space more than offsets localization of its heat bath in momentum space until a Boltzmann distribution for the molecule's altitude is attained --- and the entire (molecule plus heat bath) system is maximally delocalized in phase (position plus momentum) space.

It is all summed up in this simple equation: ΔG° = ΔH° - TΔS°

Look up "Gibbs free energy" on Wikipedia.

In principal, the conformational rearrangement between local minima for molecule/biomolecule is considered within the scope of potential energy surface. On the other hand, the transition between denatured and native state of biomolecule, or between bulk phases (solid and liquid) is addressed in terms of free energy.

Note that the representative samples of any local minima, is projected at free energy surface, by averaging over most of the coordinates.

You can also find more details in this very good paper

Potential energy and free energy landscapes. DOI: 10.1021/jp0680544