Report
A report is a statement that something occurred, made by a named source. "The IDF reports a missile strike at 18:42 local" is a report. It is true that the IDF said this. The strike itself is a separate claim.
Claim
A claim is the assertion the report is making. The IDF report contains the claim "a strike occurred at 18:42". The claim is true or false independent of who said it.
Event
An event is the underlying real-world thing the claim is about. Events are not always recoverable from reporting alone. Multiple incompatible reports can refer to the same event.
Verified fact
A verified fact is a claim that has been corroborated by independent evidence to a level that justifies treating it as established. Verified facts can still be downgraded if new evidence emerges.
Worked example
An Iranian outlet reports a strike on a named target. The IDF reports a strike on a different named target. Both reports are real — both governments said what they said. The claims are incompatible. The event is the explosion that occurred. Satellite imagery later resolves the location; the verified fact is what the imagery shows. The IDF report turns out to have been correct about location; the Iranian report turns out to have been correct about the casualty type. Both reports are real; only one claim was right; the verified fact is narrower than either.