Chain size designations e.g. 1/2 x 3/32 : how to measure? How is the second number, e.g. 3/32, determined? Do you measure:

a) the thickness of the spacer between the inner links

or

b) the distance between the inner links

I have an older bike and don't know if the chain is 3/32 or 4/32 (i.e. 1/8). It could be either. The spacer itself is 3/32 thickness and the distance between the links is 4/32.
a) the thickness of the spacer between the inner links
b) the distance between the inner links

Those two measurements are the same thing. The roller (spacer) sits between the inner plates, so its thickness is the spacing between the plates.
If you look closely at the inner links the inner edge is chamfered, making it difficult to measure the actual distance between them - I guess that's why you are coming up with different measured widths. Measuring at the roller is more accurate.
So, I guess you have a 3/32 chain.