Extract. This is a snapshot of the data. An extract (.tde or .hyper file) might be created from a static source of data, like an Excel spreadsheet. Or the extract might contain data from a relational database or from cloud-based data. Extracts that are shared on Tableau Server can be configured to be refreshed from the underlying data according to a schedule that you define.
Live connection. This refers to a data source that contains a direct connection to underlying data, which provides real-time or near real-time data. With a live connection, Tableau makes queries directly against the database or other source and returns the results of the query for use in a workbook.