I am blown away by this. I have only ever used the phrase “another thing coming.” I have heard “another think” before, but I assumed it was very much a Winnie- the-Poohesque play on “another thing.” In that way, I can only see “another think” developing later as a play on the original.
“Another thing coming” makes perfect sense in reference to the expected outcome. It means “Get ready for a surprise, because what you expect to happen is not going to happen. Something else is.”
Generally, in my experience, it is used by frustrated parents: “If you’re expecting me to give you $10 at the video arcade, you’ve got another thing coming.”