Whether a snapped belt costs you a tow or an engine comes down to one design decision. In an interference engine the valves and the pistons pass through the same space at different moments, and only the belt keeps them from meeting; break it and the pistons hit open valves, which bends them and sometimes cracks a piston. In a non-interference engine they never share space, so a broken belt strands you and nothing more. Almost every modern engine sold in the US is an interference design - it is how you get compression ratio and valve lift out of a small engine - so unless you can confirm yours is not, assume it is. That is what turns the belt interval from a maintenance suggestion into a deadline.
Both hold the crankshaft and the camshafts in step, so the valves open and close at the moment the pistons expect. Everything else about them differs.
A timing belt is reinforced rubber. On most designs it runs dry, outside the engine, behind a cover, and it ages whether you drive or not - which is why manufacturers give it a mileage interval and often a time limit as well. It is quiet, cheap to make and light, and it is a consumable.
A timing chain is steel, runs inside the engine, and is lubricated by the engine oil. It carries no scheduled replacement, which is why most manufacturers moved to chains as oil quality and interval expectations improved. That move is the single biggest reason a belt quote deserves a second look: a large majority of the vehicles on this page do not have a belt at all.
The practical difference for an owner is not the part - it is the calendar. A belt puts one large, predictable, unavoidable bill on the schedule. A chain does not, and moves the burden onto oil changes instead, because oil is what a chain and its tensioners live in.
A chain is not a lifetime part in the sense people assume - it is a part with no scheduled interval, which is a different thing. Chains stretch as they wear, and the plastic guides and hydraulic tensioners that keep them tight are usually what fails first. The symptom is a rattle from the front of the engine for a second or two on a cold start, sometimes with a timing-correlation trouble code (P0016 / P0017). That is worth investigating, not ignoring. What does not follow is replacing a healthy chain on a mileage schedule: there is no interval to follow, and clean oil changed on time is the only thing that measurably extends chain life.
Find your vehicle above. If it is chain-driven, the factory schedule contains no timing belt replacement, and that is the whole answer - bring the schedule to the conversation rather than an accusation. Check the line item first: the accessory drive belt, the serpentine belt that turns the alternator, is a genuine wear item, and "drive belt" and "timing belt" get shortened to the same word on both sides of the counter.
If it is belt-driven, compare your mileage to the interval. Near it, the recommendation is doing exactly what it should, and the water pump normally goes in the same job because the belt has to come off to reach it.
The factory schedule is one input, not a verdict on your shop. Parts fail early, and somebody looking at the car can see what a schedule cannot. What the schedule settles is whether a service is due - and that is the part you could not check for yourself until now.