CUR is an additional service, (you have to enable it ) that offers historical by-the-hour data that can offer clarity on trends and lead to a more accurate data-driven insight.
CRU are saved to S3 ( from 1 to 3 times a day) but you can also output files for Athena, RedShift and QuickSight.
With CUR you can keep visibility of costs reports older than 12 months.