I find it helpful to distinguish between "regular expressions" as something mathematical and "regexes" as nebulous more-than an NFA and less than a Turing complete grammar...DFA regex engines being the Platypus that proves the rule.

As soon as you have backtracking and capture groups it's not a regular expression in the mathematical sense. These features make regexes more useful in many simple cases at the cost of making them harder to reason about in more difficult cases.