I'm not an expert on this - and this has also been covered in some of the threads (excellent reference, BTW) over the years...But as I understand, mechanical rights are associated with the actual reproduction of the song. It's (I believe) an element of copyright - one side protects people from attempting to claim the song as theirs, the other protects people from profiting from your specific works. I believe (again, I may be entirely misinformed) that the fees attached to jukeboxes and royalties paid for due to useage of a particular recording of a song count as 'mechanical rights'.
Anyone NOT talking out their ass want in on this?
M