Have you asked for clarification from your employer as to what exactly they mean by the differentiation?

Explain that "DBA", even with adjectives like "Production" or "Project/Development", is recognized as being a very, very vague term. Ask them if they have some specific division of duties in mind, or if they would prefer you to provide that for them. Make it clear that you have an idea of what it would mean in an academic sense, but want to make sure "you're on the same page" together.

Nominally, a "Production DBA" would be responsible for server-level operations, like security, backup/restore operations, DR/BC, maintenance plans, performance monitoring (but probably not tuning), database growth vs disk space available, audits, resource monitoring (I/O bottlenecks, memory pressure, CPU use). Production DBA wouldn't touch data modeling, normalization, database architecture, T-SQL coding, securing dynamic SQL, index planning, filestream, etc.

"Development DBA" would be responsible for writing code to access data (CRUD operations), and might do architecture or might not.

Ambiguities left by that include things like, who's responsible for creating indexes? Do "Development DBAs" have any access at all to production servers, or just to Dev/QA servers? Is there a staging environment between QA and prod, and who's responsible for it if so? What about architecture and standards (normalization, naming conventions, DAL methodologies, etc.)? And others.

Get all that clarified by them. See what they mean by it, or if they aren't sure and are looking for guidance on it.