All chains “stretch” or wear out. It’s not the actual links stretching, but the bushings and pins which rotate around each other wearing out, this allows each link to pull slightly further away from each other. The cleaner you keep the chain, and well lubed, the longer it will last. Shimano chains wear out faster than most, but they’re also the smoothest shifting so I’d still recommend using them if you want smooth shifting. So, as your chain stretches, this will also wear your cogs (cassette, chain rings & rear derailleur jockey wheels).
Now, smaller cogs have less surface area to distribute the load from the chain, so smaller cogs wear out faster than bigger ones. Also obviously the amount of use each cog gets is a key factor e.g. if you never use particular gears, they won’t wear out. So, chains and cogs can wear at a similar rate or at different rates, depending on cleanliness, gear selection and cog size.
Jockey wheels don’t wear much due to chain wear, as they’re not under load (there is only load between the cassette and the chain rings on the top half of the drivetrain). The main cause of wear to jockey wheels is cross chaining (big/big or small/small).
Now you may ask, “what difference does chain wear make to how my bike works?” and that is a great question! When your cogs wear at a similar rate to your chain, your shifting will remain ok even past 1% wear. However, when some cogs are more worn than others (and the chain is quite worn), then you will start noticing some slow shifts up or down the cassette. This can’t be fixed by adjusting the cable tension. If you replace your chain, but your cassette has started to wear, then it’s likely the gears won’t shift properly. If you run everything into the ground for a long time, firstly your shifting will get bad, and finally your chain will slip over the teeth of the small cogs when under high load.
You have some options:
1. Replace the chain before it wears the cogs ~ 0.75% wear
2. Wait until the cassette is also worn out and replace chain and cassette together ~1% wear (on a road bike, the cassette cogs are much smaller than the chainrings, so the cassette will wear out well before the chainrings)
3. Run the entire drivetrain into the ground, and then replace everything - when the shifting really sucks.
For MTBs where the chain rings are similar size to the cassette, I recommend replacing chains at 0.75% wear, because at this stage the cogs will be ok. If you push it to 1% wear, you’ll have to get new cassette and chainrings. Another smart option for MTBs can be to rotate 2 or 3 chains. Give each one a couple of hundred kms and when one becomes a bit dirty, remove it, drop it in some degreaser and pop on the next chain (all clean and lubed up). Keep rotating through these chains and because each chain is only getting 1/2 or 1/3 of the amount of ride time, they’re not going to wear as quickly. It’s primarily the worn chain that wears your cogs, so they’ll last heaps longer. Then, you run everything into the ground (chains, cassette, chain rings, jockey wheels) until the shifting starts to suck, then replace it all again! However, I normally find at this stage I’m ready to upgrade my whole bike.
For road bikes, I recommend pushing it to (or a bit beyond) 1% wear and then changing chain AND cassette together. Your chain rings and jockey wheels should be fine still. You can probably do 3 or 4 chains/cassettes before you need to change chain rings, and often then just the small chain ring needs changing, depending on how much you use it compared to the big dog.