If the purchaser and registrant have different addresses, this puts the two constituents below the matching threshold and therefore will not be automatically merged. To read more about Constituent Matching, see our Constituent Matching Guide here and our Knowledgebase solution here

If the purchaser and registrant are one constituent, you can merge the two records by following the steps here. The constituent marked as Host/Will not attend contains the billing address. The constituent that is marked as registered for the event contains the registrant's address.