The Magic Band carries no personal information on it. It links to your
MDE account where the ticket information is stored. A fingerscan is used for matching the owner of the MB with the person who is using it. So, for instance, you could not purchase an AP for a child and then use it for admission to the parks for multiple children on different visits.
The child's fingerscan information, not a full fingerprint, is stored in the MDE account and is tied to that ticket after its first use.