The state transition diagram is a graphical representation of a finite state machine in an executable UML model. The states are the rounded boxes; transitions are the arrows between. Events label the transitions, and activities can be expressed as action language in the states or on the transitions.
A state event matrix (or state transition table) represents the same information in tabular form. The states are the rows; events are the columns. The transitions are expressed in the cells of the table. Note that the SEM also allows the modeler to ignore (Event Ignored) or note an error (Can’t Happen) in the non-transitional cells (state/event combinations).