26" is more of a marketing number than an engineering one. It doesn't always mean the same thing.
In particular, Sheldon Brown's law of tyre sizing applies here:
If two tires are marked with sizes that are mathematically equal,
but one is expressed as a decimal and the other as a fraction,
these two tires will not be interchangeable.
Sheldon Brown's website has a table of tyre sizes giving more detail.
So 26 × 1 3/8" is not the same as 26 × 1.375".
This is because tyres used to be sized by the outer diameter, with the rim diameter a matter of compatibility.
Modern tyre sizing uses the bead seat diameter and width, in mm. Most 26" wheels are 559mm -- almost, but not quite all of those with a decimal width. 26" wheels with a fractional width can have a bead seat diameter from 571 to 597mm. The bead seat diameter must match.
So your 26×1 3/8 tyre is probably a 597mm BSD, but could be 590mm. Your bike almost certainly needs 559mm. In modern ISO or ETRTO, you're looking for something like 35-559