There are three common job titles in the database area, which are Database Administrator (DBA), Database Programmer, and Database Architect. These titles tend to be somewhat variable from shop-to-shop, but generally the “Architect” term indicates the highest level of skill combined with considerable management responsibilities. The “Programmer” term is somewhere below that, but the “DBA” is extremely variable. I have seen shops where a person was called a DBA and filled a relatively constrained role closer to IT or operations (routine tasks, no real programming) and other shops where a person with the DBA title was basically the Architect.
There is also the Database “Engineer” which I believe encompasses the three terms that Kenneth mentions. After all, a title is just a title. What defines your professional life is your experience.