To further complicate things, 26" x 1-1/4" (597mm BSD) is incompatible with 26" x 1.25" (599mm BSD).

Q. When is 1-1/4" not the same as 1.25"?

A. When the subject is tire sizes.

There's lots of weirdness in tire sizing. Sheldon Brown does a good job of demystifying it in THIS ARTICLE on his website.