We have tons of evidence that it happened but our models for explaining and predicting it are bad at consistently and reliably explaining everything we've already seen, and each new discovery seems to break those models even more.

The theory is the model trying to explain how it works. The fact, though, is that we have evidence showing that it did happen, even if we don't have a unified theory of how it happened.

Imagine a car crash site, where the cars have definitely crashed, but everyone has different debates about what caused the crash. Imagine further that the specifics of any person's explanation has a few inconsistencies with what we see. So we'd have the fact that a car crash happened, but lousy theories explaining how it happened.