Apart from the size, is there any difference between chains for derailleurs or for single-speed / internally geared hubs?
I see a few different sizes of chain, broken down as follows

1/8 inch wide chain

 Single Speed / Internal Hub only, don't use with a standard derailleur.
 Can fit on 1/8 inch or 3/32 inch chainrings and cassettes. It will have some play when installed with a 3/32 chainring or cassette, but it's usable. So, if you accidentally buy an 1/8 in chain and have smaller chainrings, you can still use the 1/8 inch wide chain.


3/32 inch wide chain

Used for single speed or derailleur bikes.
Speced to be used for specific number of gears on the rear cassette, 6/7/8 speed, 9 speed, and 10 speed are most common sizes.  You typically want this number to match the chain (it matters more on 9, 10, or 11 speed clusters since the chainrings tend to vary slightly in width and tooth shape so they work better with the narrower spacing on the rear cassette and require more lateral flexibility.
I typically use 6/7/8 speed chains for my bikes that have single speed, fixed gear, or internally geared hubs that have 3/32 cogs since they tend to be cheaper than the 9, 10, or 11 speed chains since they don't need to be as flexible and will usually have a pretty straight chainline.
1/8 inch cogs/chainrings will not fit a smaller 3/32 chain.