Direct-Drive Vs. Pulley Drive:
Most modern generators, including all current Honda models, operate under direct drive. The engine crankshaft is directly connected to the moving parts of the generator. Here's an open-frame model that shows the engine and generator bolted directly together:
Really, REALLY old Honda generators (pre 1975) used a belt and pulley design where the engine crankshaft had a drive pulley connected to a belt than turned another pulley on the generator. Here's what it looks like:
I am not aware of any current portable generators (500 - 10,000 watts) that still use a belt-drive design.
Timing Stuff, Gears and Belts
Many small gas engines use a gear on the crankshaft to drive the camshaft. This includes all but a couple of Honda models, which use a toothed timing belt design. It's very similar to the one used in a car engine, but unlike those, the timing belt in a Honda generator is good for the life of the generator, and does not require regular replacement.
Rated "Life" of the Engine and EPA
Small gas engines are subject to EPA and California emissions regulations. Each manufacturer is required to state the expected period of time the engine is expected to maintain legal emissions levels. This is called the Air Index. Here's the chart that describes it:
Notice the "Emissions Durability" column; this the number of hours the engine is expected to provide acceptable levels of emissions. This is not the expected "life" of the engine, just the emissions durability.
No current portable generator manufacturer publishes a "life" specification, period. They all just give you X number of years of warranty, and absolutely no promise or warranty of how long the engine will last.