It would appear that a 'Database Administrator' is whatever the organization wants you to be for the role and goals to be accomplished.

In a 10-year period, I had worked for various organizations as a 'Senior Systems Administrator'. However, my role in each of those companies included database administration, and sometimes network administration or applications support. Today, I am noticing that there is a "blending" of roles such that there is no "ideal" database administrator position. One has to be "multi-lingual" when it comes to interfacing with internal customers, whether they are part of the database, systems, application, and business analyst teams.