Twyla Tharp set her sights on a Broadway success years ago, and it’s just one mark of her creative persistence that she’s reformatted the genre several times before nailing it. No surprise that Movin’ Out, which opened at the Richard Rodgers Theatre last week, doesn’t look quite like any of the previous models, either hers or Broadway’s. Possibly this is one reason critics and audiences are groping for a label.

Movin’ Out isn’t exactly a musical or a ballet or a book show. It’s not Contact, Fosse, Noise-Funk, or Stomp, or Tharp’s autobiographical ’80s dances When We Were Very Young and The Catherine Wheel, though it has links to those. It’s not Twyla meets the Beach Boys (Deuce Coupe, 1973), or the lamented Tharp outtakes from the movie Hair (1978), or her 1989 Jerome Kern ballet musical Everlast. Movin’ Out is a dance show with characters Tharp developed from the songs of Billy Joel. You get what story there is from the dancing and the lyrics. A terrific band, led by guitarist Tommy Byrnes and featuring singer/pianist Michael Cavanaugh, flies in and out on Santo Loquasto’s elevator stage to power two hours of phenomenal dancing by the cast of five principals and 12 ensemble dancers.

Movin’ Out works like a ballet and it works like a splashy Broadway production. The best of both. The dancing and the stagecraft carry you through friendship and conflict, romance, nightmare, and reconciliation. In some way it’s about the Vietnam War, but it’s more about the people who grew up in that war. Like a story ballet, Boston Ballet’s current Onegin, for instance, it concentrates on the states of mind and the relationships of the characters, not on the depths or intricacies of a plot. We don’t see the moment when Tatyana decides to marry Gremin; we see her settled down in her marriage years later, a different woman.

As Movin’ Out begins, the five high-school friends are fooling around — smooching and shoving and peering under the hood of a convertible. A parade goes by: soldiers in camouflage uniforms, cheerleaders with pompons. Next thing you know, the three guys are in boot camp, and they march into combat after that. Everything is told in dancespeak, with very little pantomime and no spoken dialogue. One of the friends gets killed in the war. The others return, and everyone experiences depression, anger, rebellion, and finally a positive reassimilation into life back home.

Tharp’s own company of ballet-trained dancers play the main characters, but the second cast, which is performing at matinees, danced with great style too, and maybe with a little more extroverted, Broadway personality. John Selya as Eddie, the tough but dumb hero, slammed into Tharp’s outrageously fast and furious movement, which incorporates moonwalking and shoulder spins, as if they were pirouettes. William Marrié, his beefier alternate, danced the part like a prizefighter. Eddie’s ex-girlfriend Brenda (Elizabeth Parkinson/Holly Cruikshank) is a party girl, a go-go dancer, and finally a grown-up match for Tony (Keith Roberts/David Gomez), who like Brenda has played around with many partners for thrills, not for love. The serious couple, James (Benjamin Bowman in both casts) and Judy (Ashley Tuttle/Meg Paul, on pointe), do get married, but he never comes back from Vietnam, leaving her a young widow.

Act one ends with an affecting scene in which an honor guard presents a flag to Judy as the band play a slow chorale. Eddie descends into addiction, becomes a street beggar, and after a series of spectacular nightmares is confronted by Judy and three other women in black with veils and pointe shoes. These reproachful Wilis somehow bring him to his senses and inspire his return to respectability. Judy and Eddie meet later on the jogging path, but Tharp resists getting them together as a couple.

I’m not into popular music, but Billy Joel’s anxious introspection about love, success, and the pitfalls of suburban life is framed in singable melodies and driving rhythms that get a grip on your sinews and your brain. Tharp compiled the songs for a high-energy throughline where the intensities and the situations change but the speedometer seldom dips below 50. Joel’s range is as eclectic as hers. He writes suave ballads ( " Just the Way You Are " ) and pre-teen ditties ( " An Innocent Man " ), acid rock, Motown, swing, honky-tonk, and angry soliloquies ( " Goodnight Saigon " ). There are a few selections from his recent album of piano solos. Tuttle and Bowman dance a tender pas de deux to " Reverie, " which sounds a bit like Edvard Grieg; " Elegy, " the act-one closer, could be the apotheosis of a Tom Hanks movie.

As for the dancing, Tharp isn’t concentrating on movement invention here. And even though the show is tied to its period (1965 to circa 1980), the styles and behaviors are more generic than individualistic. For several years in her ballets and contemporary-dance pieces, Tharp has been working on form, trying to see whether the conventional frame can hold any more than we expect. She’s been using her own virtuosic, high-speed balletic vocabulary, which is packed with steps and changes and allows almost no transitional relief.

This is the movement style of Movin’ Out. Tharp wants to put the highest-caliber, most virtuosic, most communicative dancing into the Broadway spotlight. What’s inventive about Movin’ Out is her determination to make that movement idiom serve this purpose. In allying with such popular music and, not incidentally, tapping into the sensibility of our time — the ’60s nostalgia, the obsession with war and heroism, the dread of midlife — she’s appealing to an audience that wouldn’t necessarily visit a dance theater. In recent publicity photos, Joel and Tharp look like your idealized hip suburban father and mother — he’s dapper and smiling in his little beard and black turtleneck or casual jacket, she’s gray-haired but bright-eyed behind those big glasses, in her impeccably tailored suits and blouses, and sneakers.

After one company bow, the band descend and start to play " New York State of Mind. " At the first notes, the audience screams with pleasure. It’s a great communal moment, both calculated and characteristically generous of Tharp, honoring not only Billy Joel but New York’s history, its hurt, and its survival.

Theater is always a reflection of the audience somehow, awakening our desire, nostalgia, faith. By coincidence, the Paul Taylor dance company, where Twyla Tharp started her career back in the ’60s, came to Boston’s Shubert Theatre last weekend as part of the FleetBoston Celebrity Series, offering us modern dance in polished, digestible portions. Taylor has a decade’s head start on Tharp, and I guess he’s resting on his success. His choreography seems to have settled into a comfortable, almost atrophied seniority. Maybe you can’t keep reinventing your movement vocabulary, but Taylor doesn’t seem to have had any new thoughts at all recently.

Images (1977), which opened the program, could be a sly gloss on the Greek tragedies of Taylor’s dance mother, Martha Graham. Set to eight Claude Debussy piano pieces, the dance is a series of portraits for five women and three men in quasi-Minoan costumes. They move like the icons in some severe Graham epic, with the edges worn smooth and the exquisitely incised sculptural patterns burnished by a scrupulous museum restorer. The group revolve in a tight circle with scooping arms and rounded torsos, as one person after another emerges like an idol in the center of a sunburst of bodies.

Parts of this dance used to seem strange to me, even scary. The female Oracle, for instance, who gestured with ropy arms and grew more passionate but remained fixed in place, was performed by Amy Young almost as if there were sunshine inside of her trying to get out instead of prophecy.

In Black Tuesday (2001), Taylor seems to be trying to paraphrase Company B, the successful period piece he set to the Andrews Sisters’ music. Here, he takes on music-hall songs of the ’30s and the waifs and strays of the Depression. Maybe we’re supposed to look at bread lines and down-and-out entertainers as charming tintypes — Tharp’s drug-dependent dropouts are remembered the same way. Taylor has taken many corrosive looks at the grotesques of society; romanticizing them seems false in his hands.

Promethean Fire, which premiered last summer, is exquisite and formalistic, set to the grandiose orchestrations of Bach made by Leopold Stokowski when the conductor was trying to popularize classical music in the ’30s. There were beautiful mass designs for the 16 dancers — lines endlessly criss-crossing in ingeniously mysterious ways, wavelike canons, jumping engines. At the end of part one, the Toccata and Fugue in D, the group collected on the floor into a pile-up, a familiar Taylor device signifying chaos.

Out of the heap of arms and legs, Patrick Corbin drew Lisa Viola. They danced a sculptural duet to the Prelude in E-flat minor. Then the group returned for more designs in smaller, complementary units to a Chorale Prelude. In their black velvet unisex unitards with gold stripes, the Taylor dancers looked diligent, anonymous, and uninspired. The whole enterprise seemed to be running on perfume.