I might need to replace my bicycle chain (see this question). The store where I've bought components before (cyclecomponents.com) seems to be entirely marketed to derailleurs, and I have an internally geared hub. Can I buy one of their chains as long as the size is correct, or are there some fundamental differences between the two?
I see a few different sizes of chain, broken down as follows
1/8 inch wide chain
3/32 inch wide chain
Summary: It might work. You have to check. It's easier/better to find a single-speed chain, since they're easy to find and not more expensive than a multi-speed chain.
There's actually two size differences between chains for singlespeed/internally-geared bikes and chains for derailleur bikes.
The good news is that the pitch is the same, meaning that the distance between pins is the same and the number of links in a given distance is the same.
Because of the width difference of the chain, often sprockets made for a single-speed/internally-geared bike are wider.
In other words, it might work, but it might not. Look carefully at the old chain when it's on the sprockets, and look at how the teeth fit in between the inner plates of the chain. If it looks like a tight fit with no clearance, you need a singlespeed chain. If it looks like you could almost fit a second tooth in the wide gap, you could probably make do with a derailleur-chain. Make sure to check front and back.
There happens to be two SS/internally-geared bikes in my garage, so I went and looked. One (the cheaper one) looks like the teeth are narrow enough that any chain would work, while the other has thicker teeth that just fit between the inner platesand I doubt a derailleur chain would work on it. I think it'd be fine in the front on both bikes, it's just the back on the internally-geared bike with teeth a bit too thick for that.
It probably doesn't matter for your usage, but it's also possible with singlespeed chains to get some options that aren't available on derailleur chains, such as half-link, decoratively colored outer-plates, super-heavy-duty chains, etc.
There are some other differences with derailleur chains, such as flexibility, pins, etc. But no differences that matter for putting a derailleur chain on a single-speed bike.
A derailleur-style chain needs to be more flexible, side-to-side. Not that such flexibility will cause problems on a single-speed setup. Also, newer derailleur setups need for the chain pins to project slightly, to facilitate indexed shifting. This is not needed (but harmless) in a single-speed setup.