The ones I looked at work by encoding common spelling mistakes into a grammar (as in Chomsky grammar) and then running that over the text.
If you misspelled "college" as "collage", or you misspelled "three" as "tree" the word you typed incorrectly happens to be an actual word itself! Correcting these types of errors is called "real word spelling correction".
Real-word spelling errors are words in a text that, although correctly spelled words in the dictionary, are not the words that the writer intended
https://www.researchgate.net/publication/221628953_Real-Word...
And even if there are several approaches evaluated, the problem is far from solved.
Locality: The pair "buy Apple" must be vastly preferred, like millions of times more.
Use: I'm writing this and my swipe keyboard offers "spellcasting" when I want "spellchecking". The page I'm on is about spellchecking and the other word isn't one I've ever used until now. You can split these down in to prior-use and use-context, I guess: the former is most annoying, always having to correct in the same manner.