Of the six Hollywood films of classic Rodgers & Hammerstein Broadway musicals, only one—“The Sound of Music”—was such a blockbuster hit as a movie that people largely forgot it had ever been a stage show. Of the others, “The King and I” is especially good (it’s the only one to include a star in the role he created on Broadway) and “South Pacific” is especially bad (due to the director’s bizarre method of filming musical numbers). “Oklahoma!” and “Carousel” are generally regarded as serviceable—but hardly inspired—productions of two shows that, more than any of the others, revolutionized musical theater.

Or so we thought. It turns out that when it comes to the 1955 film adaptation of “Oklahoma!,” we’ve been seeing the wrong movie for decades. The one we should have been watching has only recently been unearthed, restored, released on Blu-ray and DVD, and booked into theaters.

In 1943, “Oklahoma!” launched the partnership of composer Richard Rodgers and lyricist-librettist Oscar Hammerstein II, and created a vogue for “book” shows (in which song, dance, and story are thoroughly integrated) that continues to this day. Although the Hollywood studios started bidding for the rights to “Oklahoma!” as soon as it opened, Rodgers and Hammerstein paid $850,000 for them and started producing the picture themselves. They made a deal with the entrepreneur Mike Todd to film “Oklahoma!” in a new widescreen process he called “Todd-AO” and chose Fred Zinnemann as director, even though he had no experience with the musical form.

While CinemaScope, already in use since 1953, used standard 35-millimeter cameras equipped with a special anamorphic lens, Todd-AO required an entirely new set of special 70mm cameras and projectors. Since few theaters were equipped to show Todd-AO films, two entirely different movies had to be made: The actors would do a scene once in Todd-AO, the cameras would be changed and the actors would repeat the scene for the CinemaScope version. It was the CinemaScope film that we’ve seen, until very recently, both in theatrical re-releases and on television. That version (which is eight minutes shorter) features a very tired cast, and it shows. (Frank Sinatra walked off the set of “Carousel” a year later partly because of the extra demands of having to film that movie twice.)

The Todd-AO version, however, is fairly bursting with energy, and watching the restored Blu-ray edition reminds us of the wisdom of hiring Zinnemann—whose specialty was masculine dramas like “High Noon” and “From Here to Eternity”—rather than a director best known for musicals. The film of “Oklahoma!” is essentially a western with song-and-dance numbers that are as believable as they are spectacular; the moment when the horse pulling a buggy carrying leading lady Shirley Jones goes out of control is as thrilling as the roller-coaster ride, captured by a mounted Todd-AO camera, that can be seen on one of the featurettes included on the home-video release.