alt Hacker NewsAnd all those other parts were recovered after most flights and re-used after refurbishment on future flights. Since there's no other name than "Space Shuttle" for the whole rocket, it will do. Note that Starhsip is also ambiguous, as it refers both to the entire two stage rocket, but also just stage 2.
If you want to be precise, you can call the whole thing „Space Transportation System“. I think it was clear from context here though. The thing often called shuttle is the Orbiter.