The only thing I have ever found to work on toothache is large quantities of ibuprofen. And yes it is because it's a different kind of pain - codeine doesn't work either. I think it's because codeine, morphine, and I think cannabis and paracetamol, work on preventing the pain signals from reaching the brain, whereas ibuprofen and aspirin stop pain signals being triggered in the first place. Or possibly the other way round. Or something. I don't know why toothache is different, but it and a couple of other kinds of pain are.