cmp -s compares the full file sizes before applying the byte limit. Two files of different sizes therefore compare unequal even when every requested byte matches.

printf a > a
printf ab > ab
/usr/bin/cmp -s -n 1 a ab; echo "GNU=$?"
diffutils cmp -s -n 1 a ab; echo "uutils=$?"

GNU diffutils 3.12 exits 0; uutils exits 1. With -n 2, both exit 1 because the shorter file ends inside the requested range.