When moving a file to another volume, where does the original go? Today I moved (CMD-Drag) a folder from my laptop to my desktop across my LAN.  The resulting file (an Ableton Live project file) opened on the desktop but is missing things that were present when it was on my laptop.

I can't figure out how this could have happened, and it got me thinking... where does the "original" actually go when you move as opposed to copy something?  It doesn't just go in the trash so, is it just flagged for overwriting and made invisible?  Wondering if I can somehow get the original back.  I checked my Time Machine backups and somehow the folder in question is not there either (or actually, it's there but also missing things once restored).
The file is deleted on the spot. Which means technically it's still on the disk as a deleted file until the system overrides it. But with a running operating system, it's very unlikely you'd be able to get it back with a data recovery tool. Data Rescue does deleted file recovery, but the data you seek is most likely already overwritten.

It's also clear that the "missing" data was lost long before you moved it. Time Machine is your solution here. Keep going back until you can find a copy that is not missing the data.