What makes it specialized.
Specialization does not come from a prompt describing a role. It comes from what the agent is actually connected to: domain context, the tools it can operate, the state of the process it is in, memory of what came before, the rules it works under, the permissions it holds, and a way to evaluate whether it did the job.
A general assistant with a job title in its system prompt is still a general assistant. A specialized agent knows which case it is in.