They have striking similarities: the same boyish mop of brown hair, the same soulful blue eyes, the same oh-so-sensitive mouth. But then, there's no reason why actor Emilio Estevez, 20, shouldn't resemble actor Martin Sheen, 42. If they're not among Hollywood's more celebrated fathers and sons, it is only because one of the few things they don't have in common is their name, which suits Emilio just fine. Says he: "I didn't want to ride into the business as Martin Sheen's son."

Estevez, who next appears in The Outsiders, Francis Ford Coppola's film of the S.E. Hinton novel about high school gangs in Texas, is in fact the one who didn't change his name. It was Sheen, born Ramon Estevez, one of 10 children of an Irish mother and a Spanish father, who decided he needed a more marketable moniker 20 years ago and rechristened himself after one of his idols, the late TV priest Bishop Fulton J. Sheen. Yet names aside, the Sheen/Estevez clan is one of the closest in showbiz.

Emilio's emergence as an actor was natural, he believes: "When you're young, you want to do what your father does. As I got older, I wanted to make it a reality." Apparently, so do his brothers, Ramon, 19, and Carlos, 17, both of whom have budding film careers (sister Renee, 15, hasn't decided what she wants to be). It has been easy for Sheen's kids to get to know the trade: He insists on togetherness, demanding that his contracts provide six airline tickets, enough for all his family, when a film is to be shot on location.

The family closeness on occasion has overwhelmed Emilio, and perhaps because of it he has sometimes rebelled. Born in Manhattan, he moved West with his parents in 1968 when Sheen was cast in Catch-22. Growing up in Malibu, he rejected the local private school (it was "for parents who have everything except a relationship with their children") in favor of Santa Monica High. Emilio was 14 when he accompanied his father to the Philippines, where Sheen was shooting Apocalypse Now. For the next four months the teenager floundered, "putting away beer and hanging out in the red-light district" before insisting on returning to school back home. After graduating in 1980, he refused to go on to college and instead plunged into acting. His first role was in a drama on Insight, a syndicated TV program produced by the Catholic Paulist order. Soon after, he made his stage debut with his dad in Mister Roberts at Burt Reynolds' theater in Jupiter, Fla. "That was the only job Dad ever placed me in," Emilio says. "We were well into production by the time I acquitted myself of the sin of casting nepotism." Since then, father and son have worked together only once, in last year's ABC-TV film about juveniles in jail, In the Custody of Strangers. That time, Emilio did the casting: "I just told Dad it would be fun to work together, and one of us might be dead next week, so why waste the chance?"

Sheen notes that his son is "scrappy and cocky," and admits "that can be annoying." But he adds, "Emilio's fought for his independence, and I appreciate the way he feels. My heart says 'Do more for him,' but I have to wait for him to call me. I'd love to work with him all the time."

Right now Emilio wants "to be recognized for my own work." Besides his roles in Custody and The Outsiders, his credits include NBC-TV's upcoming thriller Nightmares and Tex, the 1982 film version of another S.E. Hinton story. He bought the movie rights to a third Hinton book, That Was Then, This Is Now, and has written a screenplay. Says Sheen: "I think eventually Emilio will have to direct to feel the full extent of his talents—his spirits are that big. He's an officer, not a soldier."

He's also no spoiled showbiz brat. He lives at home in Malibu, where his main vices are addictions to early morning jogging and health foods. When not in Malibu or on the set, he is usually with his current steady, Wilhelmina model Carey Salley, 20, at her place in Brentwood or at the Montana spread he bought with his earnings from Custody and Tex. While he has already had a rather full life for someone his age, it hasn't gone to his head. "The most significant thing my father has taught me," Emilio says, "is that my job is no more or less important than someone else's. When I realize there are a billion people in China who don't know I exist, any flightiness is swept away."