The language recognized by an automaton is defined as the set of strings that are accepted by the automaton.
I wonder if it is possible that the languages recognized by two automatons are the same? Note, if I am correct, the most general automatons are the Turing machines, and the languages recognized by an automaton are exactly the recursively enumerable languages.
The same question if restricted to the commonly-known subfamilies of languages and their corresponding automatons (e.g. regular languages, context-free languages, context-sensitive languages)?