Textbook regular expressions correspond precisely to DFAs, so they’re definitely a type of FSM.
Most Regexp implementations in the wild are more powerful than textbook regexps, so they not only encode all languages accepted by DFAs, but can also encode other languages. E.g. back-references are not a feature of regular languages.
Most Regexp implementations in the wild are more powerful than textbook regexps, so they not only encode all languages accepted by DFAs, but can also encode other languages. E.g. back-references are not a feature of regular languages.