There’s a grand irony to the life and career of Sam Shepard, who died Thursday at 73, that couldn’t have been lost on him. In the late ’60s and early ’70s, when he was first coming up as a playwright, he was part of a shaggy experimental New York theater scene, a kind of loose downtown collective that emerged from the dead flowers of the counterculture and grew into something else: a hazy ’70s druggie/poet garden of indolent creativity. It was an off-Broadway, off-kilter, semi-off-the-grid scene that sprouted up through the cracks of what had been hippie culture and would soon become punk.

Shepard wrote his plays with a wild-dog discursive freedom that would have been unimaginable before the ’60s, and his fabled romantic affair with a singer-poet named Patti Smith seemed baptized in a kind of bohemian purity. At that point, he’d already begun to flirt with Hollywood, though only as a writer, toiling away on what you might generously call the “script” of Michelangelo Antonioni’s 1970 desert youth love-in apocalypse, “Zabriskie Point.”

Then, however, a funny thing happened. Shepard kept writing plays, becoming ever more ambitious and celebrated, and just as he was hitting peak acclaim, in 1978 (the year that he simultaneously premiered “Buried Child” and “Curse of the Starving Class”), he was tapped to co-star in a major motion picture: Terrence Malick’s second feature, “Days of Heaven,” in which he was cast in the role of a wealthy, dying farmer in the Texas Panhandle in 1916 who is lured into the scheme of a pair of traveling rogues (Richard Gere and Brooke Adams). The movie was like a magic-hour version of a Biblical parable, and Shepard’s performance was wry, taciturn, sorrowful, and sexy in a gentlemanly way. As an actor, he was more than skillful enough to get by (he’d performed on stage during his theater-scene days), but in “Days of Heaven” he had something more than skill. He had an aura.

A lot of it was his look. Tall, rock-steady, almost pre-verbal, with his hair swept back and two slightly uneven front teeth that suggested the authenticity of a much older era, he could have been a preacher or a country lawyer from an age that was decades before media. He looked like a startlingly handsome man out of a 19th-century photograph. Without saying a word, he seemed to be the most genuine embodiment imaginable of an America that had long ago disappeared.

“Days of Heaven,” despite the reputation it enjoys today as a Malick classic (it was the film that really launched the director’s latter-day style of dreamy voice-over and layered image poetry — though compared to his recent films, it now looks like a work of disciplined high classicism), was not all that widely seen at the time. But what everyone who saw it in Hollywood recognized is that Sam Shepard was a new kind of old-style matinee idol: an actor the camera adored.

And so he began to get roles, playing the lover of Ellen Burstyn’s born-again faith healer in “Resurrection” (1980), one of the only Hollywood movies of the time to channel the rising passion of the New Christian Right; or as the sympathetic Communist Harry York, who becomes involved with the bold, mercurial, convention-defying Hollywood star Frances Farmer, played by Jessica Lange, in the tragic biopic “Frances” (it was on the set of that film that Shepard and Lange met, launching a 30-year relationship that was ardent and tempestuous enough to have been a movie all by itself). Shepard kept growing as an actor, and then, in 1983, when director Philip Kaufman tapped him to appear in “The Right Stuff” as Chuck Yeager, the test pilot who broke the sound barrier, he found a role he could merge with in a nearly mythological way.

If you’ve never seen “The Right Stuff,” you really should; it remains one of the most heady, exuberant, and under-celebrated American screen epics of its day. It’s not that it didn’t have its fans at the time, but the dazzling three-hour drama, adapted from Tom Wolfe’s impish but stunningly complex journalistic panorama of the U.S. space program, sprawled and reached for the stars in a way that a lot of critics couldn’t relate to. If you watch it now, it’s like a visionary mini-series you can’t get enough of. The astronauts are depicted with a humanity that has never been matched, but the cornerstone of the film’s design is the way that their globally celebrated feats are counterpointed with the off-the-radar heroism of Shepard’s Yeager, a war hero and cowboy in a bomber jacket who becomes a kind of solo space warrior when, in 1947, he goes up in his X-1 plane (with a broken rib cage, no less) and becomes the first person in history to fly at supersonic speed.

What will happen to him if he does that? He’s not sure. No one is. (Maybe he’ll combust.) So why does he do it? Because he knows that it can be done, and Shepard, who was 39 when he shot “The Right Stuff,” invested the role with a no-sweat American mettle and aging-glamor-boy daring that seemed to emanate from someplace deep inside him, earning him an Academy Award nomination for Best Supporting Actor.

The supreme, and crowning, irony of all this is that Shepard had found stardom and glory by portraying, in effect, the living incarnation of the core American values that his stage plays — the allegorical tragedy “Buried Child” (1978), the troubled and combustible psychodramatic duels “True West” (1980) and “Fool for Love” (1983) — said, in one way or another, had all gone up in smoke. He was playing the soul of an America that no longer existed. Yet he played it so slyly, with such stirring conviction and understatement, that it’s as if he marked the moment when the longing for those values — the ones shredded by the counterculture — began to make a comeback.

Ironically, the one time a movie attempted to bring the two sides of Shepard together — when he starred, along with Kim Basinger, in Robert Altman’s 1985 film of “Fool for Love” — the result was a bust. The film lacked the spontaneity and love-hate danger that had electrified it onstage, and Shepard, in the volcanic role he’d written, proved to be too laidback as an actor. From that point on, though, he settled in, appearing in a vast range of movies (“Crimes of the Heart,” “Steel Magnolias,” “The Pelican Brief,” “Black Hawk Down,” “The Assassination of Jesse James by the Coward Robert Ford”), almost always as a character who seemed to be some sort of snaggletoothed, been-around-the-world frontiersman of the spirit. His small sharp performance as a Mob enforcer in “Killing Them Softly” (2012) was one of a handful that demonstrated he could play rotters and villains too. At a certain point, even his aging rugged good looks became a different kind of signifier. You’d watch him in a movie and think, “He’s got to have something hidden going on.”

And so it was that the career of Sam Shepard, the only great American playwright who was also a movie star, became not so much a contradiction as a spectacular yin and yang. On screen, he embodied the homespun valor of our dreams — a quality that his plays told you, over and over, was too good to be true. Yet part of the powerful turbulent discord of the plays is that they never stopped dreaming of that place of solid innocence that his characters could no longer reach. That made Shepard the rare artist who dramatized American grace as memorably as he did the fall from it.