When migrating on-premises databases to Autonomous Database using Oracle Zero Downtime Migration (ZDM), both Physical Online and Logical Online migration methodologies can be employed. Physical Online migration involves replicating the physical database files to the cloud with minimal downtime, while Logical Online migration uses logical structures like SQL to migrate data, allowing for transformations and optimizations during the migration process. Both methods aim to minimize downtime and ensure continuous availability of the database services during the migration.