'Donate' seems to have the following two meanings:
1. to give something to charity
2. to give blood or a body organ to another person
Are 'donator' and 'donor' used in both meanings?
'Donator' only for 1? 'Donor' only for 2?
I'd use 'donor' for both.
"Donator" is what we call a back-formation. It's certainly in use out there, and showing up in dictionaries too. But "donor" still seems to be the ascendent choice.
Less than 600,000 Google hits for "donator"
Over 72 million hits for "donor"