This article is from the Bicycles FAQ, by Mike Iglesias with numerous contributions by others.
From: Osman Isvan <firstname.lastname@example.org >
There is nothing wrong with tire/rim compatibility. If
we...stop calling them with colloquial names such as "26 inch
wheel", "road wheel", etc., we would be all set.
There is no dimension on a mountain bike rim that is even
close to 26 inches. The ETRTO number, bead diameter in
millimeters, is *molded* on the sidewall of the tire (to make
mislabeling almost impossible) and if it matches, it will
match. There is nothing confusing, mysterious or misleading or
complicated about the ETRTO designation. The ETRTO designation
also includes the width of the tire to be sure it is not too
narrow or too wide for the rim, but this dimension is not
accurate as it is not critical.
Common standard bead diameters are 559 mm (ATB), 571 mm
(Triathlon) and 622 mm (road). They are a reasonable size
smaller/larger than each other, so what's the problem?
The confusion comes from us (marketers and consumers)
referring to both the 559 and the 571 standards, and a slew of
others, as 26" for some reason. The term "26 inch wheel"
refers to the approximate outside diameter of the inflated
tire, and has nothing to do with tire/rim compatibility...
This is no different with cars, but in automotive "lingo" the
colloquial names for wheel sizes are the rim diameter (and
that's what matters for compatibility), not the tire outside
diameter. The same car comes with either "13 inch" or "14
inch" wheel options but the outside diameter of the tire may
be the same. The rubber part takes up the difference.
Motorists refer to their RIM SIZE when they talk about wheel
diameter. A 13 inch tire such as "175/70 R 13" means it will
fit to a 13 inch rim.
We should do the same. It is possible to build the same
outside diameter by either using a 26 mm wide tire and 559 mm
(mountain) rim (ETRTO 26-559) or a 20 mm wide tire on a 571mm
(triathlon) rim (ETRTO 20-571), and this doesn't imply they
would be interchangeable. And because the 559 mm (Mountain)
rims have a diameter of only 22 inches, it takes very fat 2.0
inch (Mountain) tires to bump them up to 26". Of course they
wouldn't accept skinny triathlon tires of same thread
When ordering tires, order according to bead diameter (ETRTO
designation). This will solve any problems with compatibility.
If the salesperson doesn't understand, ask to look for the
number which is molded with the casing.