Relationship between two concepts of equivalence for finite-state machines

In the letter, the relationship between the well-known concept of `equivalence¿ and the less well known but important concept of `relational equivalence¿ of finite-state machines is examined, It is shown that, for two strongly connected finite-state machines, the two concepts are the same. Also for two non-degenerate finite-memory finite-state machines it is shown that the two concepts of equivalence are the same. These results, together with some results already known, lead to a table of relationship between equivalence and relational equivalence of finite-state machines.