(I could be wrong but this is what I understand)
1/8 and 3/32 refers to the thickness of the teeth on the chainwheel and/or sprocket, so if you have a 1/8 chainwheel, you'll need a 1/8 chain, but you can use 1/8 chain on 3/32 chainwheel/sprocket, or have 1/8 chainwheel, 3/32 sprocket and 1/8 chain.
1/8 chains (I think) were 'standard' on bikes such as 3 speed gear hubs, but multi speed rear blocks need narrower chains, hench 3/32. I'm not such why track stuff still use 1/8.