Difference between potential mean force and free energy

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Dear Users,

I used umbrella sampling and gmx WHAM to calculate the “free energy” of ions passing through a channel. In the literature [1], the free energy along the reaction coordinate is the potential mean force. However, I got below comment from reviewer saying

“Fig 5b authors report umbrella sampling simulations of single ion transport through the pore. The y-axis should be the potential of mean force rather than free energy. If they want to report free energy along the z-axis it is F(z) = U(z) -kBTln(W(z)) where U(z) is the potential of mean force and W(z) is the multiplicity, which could be estimated from the density along z for a finite number of ions at the volume slice, z.”

I am confused now as this comment contradicts with the literature. Could any one explain the difference between free energy and potential mean force?

Also, what do we get from the gmx WHAM, free energy or potential mean force?

Thanks

[1] Kästner, J. (2011), Umbrella sampling. WIREs Comput Mol Sci, 1: 932-942. https://doi.org/10.1002/wcms.66