Hi, Clément -
The headers of datasets contain things like voxelsizes and location of origin, which allow the data to have meaningful (x, y, z) locations in space. AFNI (and I guess MRIcron) use this information when displaying datasets-- they don't just match corner locations of voxels and hope for the best, for example. The voxel size, origin, and other meta-data can be viewed with AFNI's 3dinfo command.
"Orientation" typically refers to the order of arranging the data on the disk-- see "3dinfo -orient DSET", for example. That is independent of how the datasets are displayed, except for the fact that it determines what the "origin" voxel is.
3drefit is a program in AFNI that allows you to change header information without adjusting the actual data (or "BRIK") information-- this is mostly used when one assumes there is incorrect header info present, and one wants to reset it. Using this program, one could easily notice changes in how one dataset overlays another.
3dresample is a program to change both header/HEAD *and* dataset/BRIK info together, keeping them consistent. Typically, one might not see large changes in how one dataset overlays another when using this program (except for regridding/smoothing in some cases, depending on the operation).
... which is all to say, what commands are you specifically running on your dataset, causing you to see changes? And what are you wanting to do with your refitting/resampling?
--pt
