In other words, "if we build a state machine which is different from a regex, it will perform differently than a regex would." That's trivially true, but is it interesting beyond restating "there is no Silver Bullet"?
Technically we aren't discussing the regex itself here but the syntax for defining a regex.
You could use a different syntax for defining the same regex, and that syntax could have different properties. For instance you could use parantheses like racket where "(...)" and "[...]" have the same meaning, but "(...]" is not well formed syntax (if I remember my racket correctly). Using such a syntax to define regex a counter would no longer suffice to decide if a string is a regex.
