Don't apps like Snapchat notify the other person if you take a screenshot of your messages?

Yes, iOS has userDidTakeScreenshotNotification for that.

	▲	retired 2 hours ago \| parent [-]
		Would be nice if the user could disable that.

Yes, Snapchat does this. Apps absolutely have the ability to know when a screenshot is taken.

	▲	thaumasiotes 2 hours ago \| parent [-]
		Snapchat advertises that they detect screenshots. They try. But they're well aware that they can't actually know. For example, their bug bounty program policy helpfully informs you that "screenshot detection avoidance" is not considered a vulnerability: https://hackerone.com/snapchat . That's because it's always possible.