FREMONT, Calif.—A first peek inside Tesla Inc.’s new Model 3 compact car revealed a starker, cozier interior than the more spacious and luxurious Model S. But as the sedan sped off, the experience felt similar.

On Friday, the Silicon Valley auto maker showed off details of the all-electric sedan’s interior for the first time, allowing a roughly 10-minute test ride around the factory.

The Model 3 represents a milestone for…

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