Most regression testing as done by DejaGnu is system testing: the complete application is tested all at once. Unit testing is for testing single files, or small libraries. In this case, each file is linked with a test case in C or C++, and each function or class and method is tested in turn, with the test case having to check private data or global variables to see if the function or method worked.
This works particularly well for testing APIs and at level where it is easier to debug them, than by needing to trace through the entire application. Also if there is a specification for the API to be tested, the testcase can also function as a compliance test.