I agree with Jeffrey. It is not the same thing. OTT is a movie based on a Broadway musical, not a Broadway musical based on a movie. There are a lot more of the former than the latter.
AAIP may be the first hit in the Movie to Broadway route, which also includes State Fair (flop), High Society (flop), and Victor Victoria, which only ran as long as it did because of Julie Andrews, but which I think was a flop.