Many engines also use a timing chain instead of a timing belt, but this carries extra weight and requires lubrication.
It’s all about tradeoffs!
https://36.media.tumblr.com/8a928fcccf1b41e82be0273ccbe2005a...
And, given your nick, the OHC Volvo B18/B20 can't go unmentioned: Dunno if this was standard back in the day or if it was unique to this engine, but it had an interesting combination of materials. The smaller gear on the crankshaft was steel, but the larger one on the camshaft was made out of some weird bakelite-like stuff; as I recall, with some sort of fibrous reinforcement in it.
(OK, if you're not a Swedish motor enthusiast, you may be wondering "WTF does my nick have to do with that?" A: The B18 was used in the Volvo Amazon.)
I also had the machine shop at my high school weld up a custom tool to help me reset the timing belt in a parking lot with a couple of hand tools. It could be done in a few minutes.
This is a long way of saying yes, if they slip it is bad.
My Toyota actually had a small decal on the timing belt cover itself specifically for the purpose of tracking that service.
I just went through a belt change with my brother not long ago. The tolerances you're dealing with are measured in thousandths of inches. Something that wasn't installed quite straight can cause almost imperceptible wobble that can destroy things under load.
Still, every day shop tools will help you get the precision you need.
You're correct that once it jumps even 0.5cm (~1 tooth) it could touch piston to valve; it depends on the engine, but I'd wager most nowadays are interference.
Occasionally chains are used instead; more expensive and heavier, but more durable. You do need to maintain the timing either way it it will destroy the valves.
To expand: It is the teeth that make belts timing belts, they keep the 'timing' (relative rotational orientation) of 2 or more toothed pulleys. In an ICE the camshafts are locked to a 2:1 ratio to the crank shaft, in a 3d printer it keeps an axis fixed relative to the stepper motor shaft.