I agree more with philh's response that there is no alternative term for the true meaning of "regular expression" — a regular language, as suggested by _delirium, is not the same thing.

I suppose I could accept "regex" as not being a regular expression as such, but the two are used so interchangeably that maintaining a distinction isn't very realistic. I'd personally rather a regular expression described a regular language, and "PCRE" (or so) used for the Turing-complete expressions with a similar syntax.