What is the difference between 1/2'' x 1/8'' and 1/8'' chain size for single speed? I get the difference between 1/8'' and 3/32'', but does this 1/2'' really make a difference, or is it the same thing?

I want to use the chain for track cycling.
That 1/2" is a pitch, ie. distance between 2 pins, which is standard on all bikes, expect, maybe, some super vintage ones. Just forget about it and pay attention to width (1/8 or 3/32").