Moore machine
A Moore machine is a finite transducer whose output is a function of the current state alone: $\lambda: Q \to \Gamma$. While you sit in $q$, the output is $\lambda(q)$.
Arcs carry input only; the command lives inside the bubble. Entering a state “turns on” its output until you leave. On an $n$-symbol input you get $n+1$ outputs (one for the start state before any input, then one after each step).
Controllers map cleanly to Moore: states are modes (lamp level, light phase), inputs are events, outputs are commands to hardware or UI. Mealy machines put output on the transition instead; same jobs are often convertible with a timing shift.