Core Testing vs SimpleTest
The simpletest module has been integrated into Drupal 7 core. Since then the contrib simpletest module has not seen much development. See also this issue.

If you want to start writing tests for your own modules, enable the core simpletest module (called Testing in the UI) and do not install the contrib module. Also check out the examples module, it should give you an idea on how to add tests for custom code.