Infallible means he is protected from teaching error. It’s not a guarantee of truth, it is protection from error. The Latin etymology of the word is rooted in “not fail/err.” Ex Cathedra means “from the chair.” So when he exercises infallibility, we can be assured that what he says does not contain error - in a sense, that means it’s true, but in another sense, one should not believe the wording was perfect or that the doctrine he teaches can’t develop or some such. Just that it does not contain untruth.
Regarding “ex cathedra.” In order for the Pope to exercise the charism of infallibility, he must be speaking as a function of the Chair of Peter. In other words, the charism is not attached to just any day-to-day words he might utter, even as a clergyman or bishop. But he must be clear that he is exercising his Petrine roots as shepherd of all Christians, along with a few other criteria (detailed at
Vatican 1, session 4, chapter 4, paragraph 9).