A live connection asks the database for data every time a view changes. An extract is a snapshot that Tableau stores in its own fast format (.hyper) and refreshes on a schedule. Extracts help when the database is slow or busy, when you work offline, or when you only need part of the data. The cost: the data is only as fresh as the last refresh.
Switch at the top right of the Data Source page. Next to it, Filters > Add creates a data source filter: rows it removes never reach any sheet in the workbook. With an extract, filters in the extract dialog decide which rows go into the extract at all.
These filters sit at the start of Tableau's order of operations: extract filters, then data source filters, then context filters, then FIXED expressions, then dimension filters, measure filters and table calculations. That's why a data source filter changes FIXED results, while an ordinary dimension filter does not.