How do you turn off the engine on modern cars with a "START" button in stead of an old-fashioned metal-key ignition lock?

I used to repeat that line too, 25 years ago when I was still on Windows 3.x, but it's gotten a little old since then.

those buttons usually have both "start" and "stop" text on them

I find it's about fifty-fifty, not sure which side it tends towards. But I'm talking from what I've seen in Internet pictures and YouTube videos; I've only ever owned cars with metal-only ignition keys, and last I bought one, the buttons hadn't yet filtered down to my price class, so I can't recall if I've even test-driven one.