In common usage, "regex" means patterns accepted by regex engines like PCRE. Police the formal term "regular expression" if you like, but ordinary usage does not honour that distinction.
Also, it's not guaranteed that an engine implementing regular expressions will have O(n) time complexity - a backtracking engine can still have much worse performance on formal regular expressions.
Also, it's not guaranteed that an engine implementing regular expressions will have O(n) time complexity - a backtracking engine can still have much worse performance on formal regular expressions.