I think you’re confusing “regular expression” (RE) for “deterministic finite-state automata” (DFA).
“Regular Expression” is just the name for the grammar/formal language model that REs present. REs are a useful way to encode DFAs, but not all things that can be expressed using RE formal-language are DFAs.
Some REs (i.e. the “Perl-compatible” or “extended” Regular Expressions) are Nondeterministic Finite-state Automata or “NFAs”. This doesn’t change the fact that the language used to express them makes them Regular Expressions.
“Regular Expression” is just the name for the grammar/formal language model that REs present. REs are a useful way to encode DFAs, but not all things that can be expressed using RE formal-language are DFAs.
Some REs (i.e. the “Perl-compatible” or “extended” Regular Expressions) are Nondeterministic Finite-state Automata or “NFAs”. This doesn’t change the fact that the language used to express them makes them Regular Expressions.