At a virtual product launch in November for Apple’s Mac reboot, actor John Hodgman appeared in a nerdy, ill-fitting suit before a white backdrop. "Stop, hang on, wait, one more thing, hi, I’m a PC,” he said, reprising the popular Mac vs. PC television commercials of a decade ago that not so subtly telegraphed the idea that Apple was cool and Microsoft wasn’t.

The event was held to let Mac fans know the new machines were getting a processor with more sizzle. But the subtext was unmistakable: Apple Inc.’s old rivalry with Microsoft Corp. was back.

For several years, the two companies had found reason to collaborate. Microsoft’s Office and other apps began appearing on the iPad and iPhone; Apple even invited Microsoft to a product launch. Apple recently made it easier to use Xbox game controllers on Apple devices, while Microsoft made its products compatible with such new Apple features as the Apple Pencil and Magic Keyboard. Last fall, Apple even put its TV app on the Xbox.