Where an export is everything in a date range, an evidence package is a bundle about one issue — a run of missed handoffs, a disputed expense — with the relevant entries pulled together and the verification included.
It's easier to hand someone than a full history, and easier for them to read.
Build it around a question, not a person. "Handoff times, March to June" gets read. A package assembled to prove someone is a bad parent tends not to land the way people hope.