What is the difference between 1/8 and 3/32?

Why do I get the feeling I am going to regret reviving this thread?

New bike comes with 1/8 chainring, 1/8 chain and 1/8 fixed cog, and looking to put a White Industries Dos Eno double freewheel on other side (I don't ride fixed, and having a bit of flexibility in gearing suits what I want the bike to do)

Trouble is the Dos Eno freewheel is 3/32 - with switching between the two cogs chainline may never be perfect, and biggest fear is whether this will be enough to affect drive, or end up derailing chain

1/32 is a tiny difference in chain width, but is it going to screw up my plan for a simple ratio change? next best option is a custom free/free hub (Phil Woods or similar) but the tyres I plan to run are directional so not really an option

Any suggestions

A 1/8" chain is designed to work with a straight chainline.

A 3/32" chain is designed to work with derailleur gears which means an often staggered chainline. It will flex more easily than a 1/8" chain to allow this.

Given that the chainline will always be slightly off with the Dos you can see why they went for 3/32".

A 1/8" chain will happily sit over a 3/32" cog and will have some side to side play - possibly enough to allow for the difference in chainline but depending on how close together the cogs are a 1/8" chain may foul the larger cog when used on the smaller one. (Try putting a 1/8" chain onto a 9 or 10 speed cassette to see what I mean).

So, it'll probably work with an 1/8" chain, would almost certainly work better with a 3/32" chain but will never work as well as a single cog/perfectly straight chainline regardless of what chain you use anyway.