Every order creates a licence key the moment payment completes. You will find it under My Account, in the Licence keys tab, with the number of sites it is currently active on.
Single Site keys cover one website. Extended keys cover unlimited client websites. To move a Single Site licence, deactivate it on the old site and activate it on the new one.
Keys also unlock downloads and updates. If an order is refunded, its key is revoked and the download is no longer available. The full details are in the documentation.