Wheel I got off craigslist
 

I don't know if this is normal or not, but here's the story
I got an old bike to fix up and turn into a commuter fixed gear/single speed with a flip flop hub. I didn't know vertical dropouts were a bad idea before, but I'll deal with that when I get to it.
Anyways, so this bike used 36 hole 27 1 1/4 wheels. I couldn't find a flip flop hub that I could use for it, so I opted to just upgrade to some more modern 700x23cs and sell my wheels. I picked them up yesterday, and it was all good.
I didn't think to check while I was buying it, but a little while after I got home I checked if the freewheel and fixed gears were 3/32 or 1/8.
Well... The singlespeed cog is 3/32. But the fixed gear is 1/8. Is that normal?

It won't make a difference if you use a 1/8" chain.

Yes. If you want to be thrifty and an effective rider, just run a 1/8" chain. If the cog being slightly smaller REALLY disconcerts you (it doesn't actually matter, by the way), you'd need to purchase a 1/8" cog. Its really not worth it in the grand scheme of things, but I won't fault you if you learn that by experience.

wouldn't it be cheaper to just buy a 3/32 fixed gear? I've heard running a 1/8 chain on a 3/32 cog and crank leads to the chain coming off more often.

If your chain is repeatedly falling off, it's not going to be because your cog is a 3/32. It's probably a silly thing like chain tension or your nut slipping in the dropouts.

So. Many. Words.

You'll be fine. Srsly; stop arguing.

Having your nut slip is no good.

nope.

I wouldn't worry about the cogs. The real concern is whether you can get proper chain tension with the vertical dropouts. If a chain fits, great. If not, your only option is to try a half link and see how that works. If that doesn't work, but a tensioner on it and run in freewheel mode.