Typically, you would use the Group option to transfer a full copy of data from a Source table(s) to a Target table(s). Group tables in a DB usually include lookup tables, referene tables etc, that need full copy of data for the application to function correctly.
Entities are usually used to perform a subset e.g. only transfer a smaller copy of data from the source to the target. E.G. if I work on Bank system, maybe I want to select 5% of Mortgages from Production, to populate my QA target DB for testing. (instead of transferring the full 100% copy of mortgages, to reduce volume of data in QA)