Difference between "OK" and "okay"

Solution 1:

"Okay" is listed as a variant spelling of "OK" in my local dictionary. This previous answer has a good description on the origin of "OK":

According to the OED, it's an initialism of oll (or orl) korrect, first seen in 1839.

I suspect that "ok" is not listed as an acceptable spelling because the origin of the word was "OK" due to its being an initialism. The variant of "okay" is just how one would spell a word with the same pronunciation. With "OK" and "okay", there isn't much need for "ok".

Solution 2:

O.K. was probably the first spelling (and there are dozens of theories about its origin). OK is an obvious shortening, maybe by somebody who had only heard the phrase. But ok would be something different, perhaps a small okapi. That's what your spellchecker thought wasn't okay.

Edit: O.K. is pronounced 'okay', and so is OK. But ok would be pronounced 'ock'.