Apple Inc. became a colossus by redefining gadgets including the smartphone, the tablet and the smartwatch. As it takes aim at Hollywood, it is working from a very different script.

On Friday, the company plans to launch the Apple TV+ video service, its contender in the battle between media and tech giants for people’s streaming dollars. Apple TV+ is slated to start with nine programs, including a buzzy drama about television news called “The Morning Show” featuring Jennifer Aniston, Reese Witherspoon and Steve Carell. Other...