Payment rules has approval and permissions to ensure your payment goes to the right person for visibility and approval.
Transfer rules allows admins and owners to set an approval hierarchy for all Vault users.
You can set rules based on the following:
Amount being sent
Role of user sending the transfer
Role or user who you want to approve the transfer
You can add up to 5 approval steps
Within each step you can select that all users in that step need to approve or only one user in that step can approve.
See video below to learn how to set up single or multi-step transfer rules within Vault: