I mean, the whole point of regexes (not to be confused with PCREs) is that any given regex is isomorphic to some canonical finite state machine. It is, specifically speaking, a tiny description of an FSM over the alphabet of ASCII characters (or whatever charset you're using).

Interestingly, regexes/FSMs are (IIRC) the most powerful class of machines for which equivalence is decidable. So if you give me any two regexes, I can tell you if they match on all the same strings, but this is not true for any more powerful grammar.