What is the difference between live and extract connections

Live and extracts are two ways you can make the data connection to the tableau. Live allows you real-time data while extracts are kind of batch which needs to be refreshed from time to time to get the updated data.

So, in the case of live connection whatever changes will be done at the Datasource end that will be directly available to the tableau desktop.

While in case of extracting any changes made in the data source won't reflect in the report immediately. It will be reflected when the extract will be refreshed.