Find or invent a term for "Completely intersecting minus one"

Your situation reminds me of the Latinate word penultimate meaning “next to last,” from paene “almost” + ultimus “last.” You could combine the pen– prefix with another suitable Latinate word: penequivalent.

It looks like you are matching nucleotides, so I'm guessing this is related to bioinformatics. While I'm not conversant in the subject, I did come up with the term contig (as in "contiguous").

A contig (from contiguous) is a set of overlapping DNA segments that together represent a consensus region of DNA.

In the description of consensus sequence (link from consensus region), there is a discussion of notation for describing the quality of a match.

I would suggest you might try something like this:

"The strings R1 and R2 are contig(3,2)."

This would mean the strings are length 3 and have a contiguous match over 2 characters.

I don't know if this would create confusion with the existing use of "contig", but if you lay out this definition somewhere in an introduction, the reader should be able to follow.

If you are only interested in contiguous mismatches that are off by 1, then you might coin a shorthand term, like "R1 and R2 are contig-1".

The term for two sets that evaluate to be equal is coincident.

To describe your circumstance I believe the phrase coincident less one can be turned effectively.

This also easily generalizes to any small number of exceptions from coincidence.