I'm not sure how it works for the jet guys, but after a helo bubba passes his instrument checkride, he can go take the FAA exam (which nobody has failed in 17 years....). Upon winging, he gets his FAA single-engine airplane land (instrument and commercial) and his rotorcraft - helicopter (instrument and commercial). If you went through Vance, I believe you get a multi-engine (centerline thrust restriction) airplane rating instead of the single-engine airplane. ("Land" refers to a regular airplane in contrast to a seaplane.)
To answer your question, after that you can go rent a single engine airplane (helos are WAY too expensive to rent.)