Don Cheadle as Miles Davis in "Miles Ahead." (Brian Douglas/Sony Pictures Classics)

Miles Davis and Nina Simone worked together only in the sense that they occasionally toured together — and not to particular success. “The Miles Davis-Nina Simone show . . . laid the worst egg in some time,” reported Variety of their double-billed Northern California dates in March 1960.

Trumpeter Davis (who died in 1991 at the age of 65) and singer-pianist Simone (who died in 2003 at 70) weren’t really stylistically compatible, which may explain their touring failure. Simone, whose palette extended from classical and standards to rock-and-roll and her own originals, was labeled “jazz” mostly for lack of a better term. Davis defied the term as well, comparing it to a racial slur, but he unmistakably developed within that tradition.

Each musician is the focus of a new biopic — Don Cheadle’s “Miles Ahead,” starring Cheadle as Davis, came out April 8, and Cynthia Mort’s “Nina,” starring Zoe Saldana as Simone, is due out on April 22. The close timing of these releases is serendipitous not only because they’re both respected jazz musicians, but also, paradoxically, because of their shared resistance to categorization. (Another jazz biopic, the Chet Baker story “Born to Be Blue,” was released on March 25, but Baker stands apart — not least because he happily defined himself as a jazz player.)

Davis’s starting point was in bebop, the revolutionary jazz of the 1940s associated with saxophonist Charlie Parker and trumpeter Dizzy Gillespie. Davis idolized Gillespie and played in Parker’s band, but his restlessness soon led him to pioneer a new style (cool jazz), then another (hard bop) and another (post-bop) and another (jazz-rock fusion).

“People ask me why I don’t sound like I used to,” Cheadle’s 1970s-era Davis tells Ewan MacGregor’s reporter in “Miles Ahead.” “I say, ‘Well, what’d I used to sound like?’ Music that isn’t moving forward is dead music.”

David Oyelowo and Zoe Saldana in "Nina." (Courtesy of RLJ Entertainment)

Simone’s unique sound, by contrast, was fully formed almost from the beginning of her career: In 1954, 21 years old and working in a small bar in Atlantic City, she was already attracting attention by melding classical piano with jazz, folk, gospel and R&B tunes, as well as a low-register vocal delivery that was equally distinctive.

“She was one of those musicians who . . . if you hear them once, the next time you heard them [in another song] you’d say ‘Oh, that’s that same one I heard last week,’” says writer Stanley Crouch in Liz Garbus’s 2015 Netflix documentary “What Happened, Miss Simone?” “Nobody sounds like that except her.”

Davis and Simone were both victims of racial discrimination: Davis was beaten by a white police officer in 1959, an event reenacted in “Miles Ahead.” Both were also dark-skinned African Americans and talked openly about how that deepened the stigma they felt. (Even before production, “Nina” courted controversy with its casting of the light-skinned Saldana, who wore makeup to darken her features.)

Both artists engaged in the struggle for civil rights, albeit to varying degrees. Simone was more active, both in her music as well as in the movement. In 1963, she wrote and recorded “Mississippi Goddam,” a reaction to the murder of four young girls in a Birmingham, Ala., church bombing, breaking new ground with its explicit condemnation of white supremacy. Later she would write and record “Young, Gifted and Black” (1969).

Simone was a militant, an advocate of Black Nationalism who once repudiated the Rev. Martin Luther King Jr.’s philosophy of nonviolence to his face. She became so close to Malcolm X’s widow, Betty Shabazz, that her children called her “Aunt Nina.” Though her activism was heavy enough to reduce her musical output significantly, she became one of the icons of the movement and the era.

Davis’s direct involvement was rather less. He did perform a February 1964 benefit concert in New York for the NAACP, the Congress of Racial Equality (CORE) and the Student Nonviolent Coordinating Committee (SNCC), recordings of which spawned two of his greatest albums.

But the trumpeter’s larger reaction to racial inequality was more personal. He refused to defer to his audiences, turning his back onstage for entire concerts and neglecting to speak to them onstage or off. While he did this for both black and white audiences, he intensified his contempt for the latter. Davis even criticized his heroes Gillespie and Louis Armstrong for their willingness to mug for the white crowds (“tomming,” as Davis called it). Still, he demanded respect from the white music industry, strongly asserting himself on issues of payment and ownership — a concern reflected in “Miles Ahead.”

In the age of civil rights, that attitude helped make him, like Simone, an icon to white and black fans alike. “All of a sudden everybody seemed to want anger, coolness, hipness, and a real clean, mean sophistication,” Davis recalled in “Miles,” his 1990 autobiography.

Davis’s behavior, however, became erratic and violent. In this he shares another connection with Simone, who in her later years was diagnosed as being manic-depressive. Her instability features in “Nina,” which begins with her being institutionalized. Davis’s mercurial temperament is the fulcrum of “Miles Ahead,” which focuses on the trumpeter’s unhinged quest to recover a stolen tape of his last recording session. It also takes place during his abortive five-year retirement from music, during which Davis admitted taking copious amounts of cocaine.

But “Miles Ahead” turns Davis’s volatility into a cartoon — Cheadle plays him as a gangster, firing a pistol around Columbia Records’ offices and partaking in a wild car chase around Manhattan. Davis wasn’t really a gun-waving maniac, with or without cocaine (although he would probably have enjoyed seeing himself played as one). But he did recount having once threatened Charlie Parker with a broken bottle, and he punched John Coltrane, then a member of his band, when the saxophonist arrived at a gig late and high on heroin. He was also an abusive husband to his first wife, dancer Frances Taylor. Even when he wasn’t violent, Davis was intense and often angry, and the film trades on these traits even as it exaggerates them.

Simone did have a history of gun violence. “Nina,” too, features the artist pointing a gun at a record executive; in her case, though, it is (loosely) based on a true story. She fired a shot in Switzerland in 1985, at a man she believed had stolen royalties from her. “I got a gun . . . and I followed him to a restaurant and I tried to kill him,” she told BBC News in 1999.

Simone was in an abusive marriage as well, though on the receiving end, regularly beaten by her husband, Andrew Stroud. This apparently contributed to her alcoholism, as well as a series of nervous breakdowns and manic episodes, all of which turned her from the abused to the abuser, says her daughter Lisa Simone, the target of the abuse, in “What Happened, Miss Simone?”

“She could get violent. The change in her would be dramatic,” her friend and guitarist Al Schackman says in the Netflix documentary. (“Nina” avoids Simone’s abuse of her daughter.)

It’s no surprise that such outsized personalities would be big-screen stuff. But the music is where the biopics fall short.

Simone’s music reflected her character: passionate, powerful, forthright, as if the singer were incapable of holding back. “Nina” does a fairly good job of making this point, though Simone’s music remains far too much in the background.

Davis, on the other hand, held everything back: His was a music of reserve, of cool detachment, and what it did betray was a vulnerability that Davis the man would never have demonstrated. These are qualities that deserve to be examined on film, too.