What does a diff checker do?
A diff checker compares two versions of a text and shows the smallest set of changes that turns the first into the second: which lines were removed, which were added and which stayed the same. The name comes from the Unix diff command, and the same idea powers version control, code review and the track changes view in word processors.
Finding that smallest set is equivalent to finding the longest common subsequence (LCS) of the two texts: the longest run of lines that appear in both, in the same order. Everything outside it is either a deletion from the original or an insertion in the new version.