Spell checking is distance between a word and the closest word in a set. But it's not like the set of allowable spellings for words is well-defined. You generally choose a dictionary (or /usr/dict/words) and call that canonical-enough. Which dictionary you use, and whether your spelling is actually a better choice for your context than what the dictionary says aren't generally considered. Even though they do fuzz the idea of what's properly spelled.

EDIT: I'm not trolling or trying to start a flame war on spellers. Just point out that almost every part of human life has some subjectivity to it.