FAs = Finite Automata = Finite State Machines = FSM
Finite Automaton accepts a Regular Language
Simply put, FSM (Finite State Machine) differs from a Turing Machine in that it has a finite number of states and produces output through a state graph based on incoming input
Finite Automata
Visualization
Finite Automaton
This is a drawing of a toy parser finite automaton, probably generated by Yacc. The rankdir=LR attribute requests a left-to-right drawing, oriented in landscape mode. Note the use of text labels on edges. Computation begins at node 0, and ends at "accept state" nodes, marked with double-circles.
http://www.graphviz.org/Gallery/directed/fsm.html

Seonglae Cho