The correct format to access or use tables in the Unity Catalog is catalog_name.schema_name.table_name. It's important to note that in the Unity Catalog, 'Database' and 'Schema' are terms that are used interchangeably. Additionally, a catalog is registered under a metastore. By default, every workspace comes with a default metastore named hive_metastore. Unity Catalog enhances this by allowing the creation of metastores that can be shared across multiple workspaces.