Why is it essential that the same restriction enzyme be used to cleave (cut) the DNA of both organisms used to create a transgenic organism?
There are certain compatible restriction sites that can be used together. Xho1 and Sal1 are examples. Their sticky ends match, and so they can be ligated together. But ligation kills both Xho1 and Sal1 site, so you can't use either of these to cut with again (at the ligation locations).
You can also use exonuclease or PCR to make most sticky ends (5
or 3 overhangs) into blunt sites - in this way you can ligate into a blunt cut site - but this will generally kill the blunt site, as well.