DBA working on production database - Production DBA
DBA working on development site - Application DBA or development DBA

Depends on where a DBA is working.

For a big company with huge databases the DBAs are divided. Like DBAs for Tuning the database, DBAs for taking care of backup strategy, DBAs taking care of Application.
DBAs for doing the setup and system testing, DBAs doing volumetric testing.

In a small company one DBA takes care of the whole thing.

So i think the discremination is scenario based.

inputs from others are welcome