I am not an expert on the old OpenFMRI derivatives scheme, so I invite correction, but here’s how I would read these:
bold.nii.gz - Original BOLD series
bold_mcf.nii.gz - Motion-corrected BOLD series
bold_mcf_brain.nii.gz - Motion-corrected, skull-stripped BOLD series
bold_mcf_brain_mask.nii.gz - Binary volume of voxels in/out of the brain, in BOLD space.
I would expect that
bold_mcf_brain.nii.gz is exactly
bold_mcf.nii.gz, masked by