MIDI tuning in Pro Tools vs. Reason

[Chordless]

I discovered something rather odd just now. I am using Rewire to run Reason 2.5 through Pro Tools 6.0 (Digi 001). I recently learned that I could set a Pro Tools MIDI track's output to be a Reason device. Previously, I was comparing my keyboard's internal piano sounds to Reason devices' sounds by first digitizing the Pro Tool's MIDI track (creating a piano audio track), and second recording the same MIDI line into Reason's arrange window to hear the Reason devices' piano sounds. Well....it turns out that if I play Pro Tool's MIDI through a Reason device, the tuning is different than if I record that same MIDI in Reason to play it through the same device. This is so odd - isn't the MIDI command for, say, a C note, the same exact combination of 0's and 1's no matter what the software program??? This makes no sense to me. I now need to go back to my previous way, otherwise Pro Tool-generated MIDI playing through a Reason device will clash, tuning-wise, with Reason MIDI playing through other Reason devices. Thoughts? Seems like I'll have to stick to either using *only* Pro Tools' MIDI, or *only* Reason's MIDI. This is a pain, because I'd already laid down MIDI tracks in Reason before discovering the Pro Tools trick. Thoughts?