On general, you must cancel your reservation at least one day in advance. Originally, it used to say that reservations must be cancelled by 11:59 pm on the day before the reservation, but that language was removed from the website. So, I asked a couple of different times to see what "one day" meant and could not get a definitive/consistent answer. Some CMs said it meant 24-hours before the reservation (e.g., by 5:00 pm on Monday if your reservation was for 5:00 pm on Tuesday) and other CMs said it meant anytime the day before (e.g., anytime on Monday if your reservation is on Tuesday). To be safe, I'd go with the 24-hour interpretation.
As far as I know, character dining and non-character dining have the same cancellation policy.