[wooter]

Remixed can be as easy as taking the original recording and feeding it back through the mix, using processors to possibly clear up and change the sound.

Remastered is taking the original recording and master it again.

Remastered from MIDI is a bit weird, indeed. I think what happened is that they had the original MIDI files (which are relatively easy to keep) but MIDI only records timing and MIDI commands to MIDI enabled instruments. So if you lost your old trusty sampler and original samples, you'd need to resample and reprogram your sampler. If you lost your trusty synth and it's presets and modifications you saved, you'd need to find a way to recreate these sounds on a similar or other synth.