The other is the actual MIDI performances. Almost all performers copyright their MIDI files, using the argument that they are an original performance of a classical work.
I'm not sure how MIDI works. If you give two MIDI composers the exact same sheet music, would there be differences in the files they generated? In other words, does they basically just enter the sheet music and a music file comes out, or is there a task of arrangement that produces a unique file no one else could create exactly on their own?
MIDI basically records the instruments used, the note sequences, and their timings: so you could presumably convert a music score to a MIDI file by software. No creatibve input required, but you'd just have a mechanical performance. Or you could capture the performance of a live musician: all the subtle or not so subtle timing variations that distinguish that person's style and make it sound unlike a mechanical performance. Whe you do that, you have a file that is is a recording of that person's performance, just as a CD or tape or 78rpm disk is a recording of what that person's performance sounded like. You or I (even if I could play an instrument) couldn't recreate that data from the score. An interesting item on grabbing performance data from recordings: http://edwardwillett.blogspot.com/2005/05/live-performances-from-dead-pianis...