My impression is that surface area is literally that, if the cortical mantle was spread out into a sheet what would the surface area at. The folding instead is the pattern of folks that make of the gyri. Neither are measures that most labs look at when using Freesurfer (thickness and volume are most common). I would take a look at this paper to get a sense of what Freesurfer means by cortical folding.
I have a more detailed idea now about what cortical surface area is in a methodological sense. What now interests me is, what does cortical surface area stand for?
As for example cortical thickness is an indicator of number of neurons per cortical column. What neurobiological characteristics are connected to cortical surface area?
Further, one would think that cortical surface area is perfectly correlated with cortical folding. Is that true? Do you have any experiences?