Difference in fMRI files

Can someone describe the following files and their differences in fMRI data?

bold_mcf_brain_mask.nii.gz
bold_mcf_brain.nii.gz
bold_mcf.nii.gz
bold.nii.gz

For example, these files are here:
BOLD files

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 bold_mcf_brain_mask.nii.gz.

Thank you very much effigies, it clarifies things.