Originally Posted by harryr
Of course the rim size matters. For the same size tire, it changes the diameter by one inch.
What would be an example of a same sized tire for a 15" and a 16" rim?

I think people might be referring to original size tires available on original rims. 1947-1955 1/2 ton trucks could be ordered with 15" wheels/tires or 16" wheels/tires.

In 1952 (for example), the optional 15" wheel/tire combination was a wider diameter than either/both of the 16" wheels/tires combinations (standard or optional).