The Mazda 3 timing belt or chain question is a common one, but one with a fairly simple answer. Unless the Mazda 3 in question is the very first turbo-diesel model (sold in Australia between 2007 and 2009) then the engine powering it uses a timing chain rather than a rubber belt.
The exception was the 2.0-lire turbo-diesel which used a rubber, toothed timing belt. The design seems sound, however, and Mazda’s recommended replacement interval for the belt and its tensioner is every 120,000km. Make sure this has been carried out promptly, as a snapped belt will probably destroy the engine. A small sticker somewhere in the engine bay should record the most recent belt change. The complete kit to replace the timing belt on this engine is available for around $200 and you should budget another few hundred dollars to have the job carried out by a workshop. Best practice is to also change the water pump and thermostat at the same time as these live in the same area of the engine.
The task of the timing chain or timing belt is exactly the same: They take drive from the engine’s crankshaft to the camshaft and, in the process, keep all the moving parts in harmony. Many car makers moved away from a timing chain to the rubber, toothed drive belt as a way of simplifying engine design and driving down the cost of each engine. The rubber timing belt is also quieter in its operation and is also less prone to stretching (as a timing chain can) so the camshaft (commonly referred to as the cam) stays in perfect synch with the rest of the engine’s rotating parts. The rubber belt is a simpler design because it doesn’t need to be tensioned via oil pressure from the engine as many timing chain systems are.
The timing chain, meanwhile, is preferred by some manufacturers because it should last the lifetime of the engine and never need replacement. This isn’t always the case, however, and some engines designs from a variety of manufacturers suffer problems in this regard. But, in a properly maintained engine of sound design, the timing chain should never need attention, while the rubber timing belt generally has a replacement interval of between 60,000km and 120,000km, depending on make and model.