Probably never because the industry almost completely transitioned away from belts to chains over the '00s because consumers hated having to do a multi thousand dollar service as preventative maintenance every 100k or so.
This must be unique to the US, many vehicles in Europe still have a belt. Even with a chain you'll probably still have auxiliary belts which need replacing, water pump, etc.
For small engines, a manufacturer will use the same one everywhere in the world with very little difference. Only when you get to large engines do you see things unique to the US.
The issue with belts/chains is if the engine is designed for interference or not. If the belt/chain breaks do the valves and pistons come in contact with each other or not? That's a design decision with costs and benefits.
With an interference engine, a broken belt means a destroyed engine - preventative maintenance is mandatory. Or you go with a timing chain.
If you don't have an interference engine, you replace the broken belt and drive away. Preventive maintenance is a good idea but not quite so critical.
Interference engines can run with much higher compression ratios and get better performance for their size. So you see more timing chains with higher performance engines. If your car doesn't have a turbo and isn't aimed at the speed racer crowd, chances are better that it has a timing belt.
They'll use the same engine, but quite often different engines are available in different territories. I know that the VAG 1.5 TSI (used in lots of cars here) still uses a belt for example, but the 2.0 TSI is chain. Perhaps in America only the 2.0 is available.
