Both are forms of intensity normalization, but they're not interchangeable (not equivalent).
My impression is that most people (in fMRI) prefer _not_ to do global normalization, but that's at least somewhat debatable.
In global normalization, the factor you use to normalize a given voxel at a given timepoint is the average over the volume. Specifically, SPM uses a rough criterion to decide what the in-brain voxels are, then takes the mean over those voxels (_for that time point only_), and uses that mean to do the intensity normalization.
In grand mean scaling, you use the mean over all the voxels and all the timepoints in the run (aka session).
So in global normalization, you only use the "space" mean. In grand mean scaling, you use the "space-by-time" mean.
There's also minor details, like multiplication by a constant. E.g., I think in GMS the constant is 100, so that units are percent change (not fractional change).
NB: neither global normalization nor grand mean scaling leads to statistical estimates with units of true local percent signal change. GMS has units of "percent change," but it's not truly localized. (Whether that matters is another story.)
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