If you have set Teracopy to verify upon moving and copying, original and copy should be identical. You can automatically save the checksums for re-verification later on.
Transferring (moving) or copying?
It's better to copy, so you retain your original as a "backup," in case something goes wrong at some later time. Then you can always re-check integrity in the future.
I use Beyond Compare on whole drives/volumes to compare/verify integrity and re-synchronize/update from time to time.