If the performer is either the original performer or a member of the original band or one of the writers, then it is not a cover.
For all edge cases, is a case by case discussion.
But as @fmera said in Edit #21155965 - MusicBrainz :
on a side note, i wish the editing system were set up so all you need to do is identify the original version and set that as ‘original’, since there could only be one original. then all the rest, less those specifically identified as ‘‘not’’ covers, would automatically be ‘covers’ w/o editors having to do anything. saves a ton of cleaning up/editing work. the present way is tedious.
It would be so very much better and sustainable.
It would be similar to the work relationship premiered at.