Depends on the company, I have worked as both production and development DBA.

Development DBA's tend to be more development focused, working with developers, core skills more focused on T-SQL, writing triggers and stored procedures understanding performance tuning. you are expected to know advanced T-SQL and have more knowledge than developers regarding SQL.

Production DBA's more focused on administration of existing systems, keeping them running at peak performance. you generally dont create anything, more support than anything else.

Developers normally graduate into a development DBA role, as it is similiar to what they do normally. Development DBA's dont normally have access to live production servers, that is what Production DBA manage normally.

In some organisations, there are split teams, a development dba team and a production dba team, all with separate sql estates that they manage. but some small organisations, the dba team might manage all environments and be responsible for production servers and development servers as well.