Transducer
Also known as: Finite transducer
A transducer is an automaton that produces an output stream while it runs, not just accept/reject at the end.
Finite transducers still have states, an input alphabet $\Sigma$, and transitions. They also have an output alphabet $\Gamma$. Moore attaches output to states; Mealy attaches it to transitions.
Accepters (DFAs, NFAs) answer language membership. Transducers drive motors, lamps, UI modes: $\Sigma$ is events, $\Gamma$ is commands. Same finite-state discipline, different job.