How does git diff tell if a line has been modified or added?

Given two files how does git diff or any diff tool tell which lines have been added, modified or deleted?

Are there any edge cases where it may fail to recognise the correct status of the edited line?

EDIT: This question is more concerned with the actual method of how the diffing happens

Git stores snapshots: given any two snapshots of your choice, Git extracts the files you'd like compared¹ to a temporary area² and then runs a "diff engine" on the two files. The result of this engine is, or should be, a series of instructions that, when applied, will convert the left-side file to the right-side file.

Git has several built-in diff engines, which Git calls:

• myers: This uses an algorithm by Eugene W Myers with some slight modifications. There are numerous StackOverflow questions and answers about Myers diff: https://stackoverflow.com/q/42635889/1256452; https://stackoverflow.com/q/805626/1256452 (multiple answers but several about Myers diff); https://stackoverflow.com/q/52721286/1256452

• minimal: same as myers but without some modifications done to go faster instead of more-minimal when the divide part of the divide-and-conquer starts behaving badly due to very long edit scripts. In a sense, this is the real Myers algorithm.

• patience: Bram Cohen's algorithm; see the accepted answer to https://stackoverflow.com/q/2817255/1256452

• histogram: a modification of patience aimed at not accidentally synchronizing on things like brace-only lines.

It can also run your chosen external diff engine.

¹Or at least, the ones it wants to compare. If you are comparing files that are not actually in commits, they may already be extracted.

²Git mostly does this in-memory, but when running an external diff, really does use temporary files.

git keeps the current committed version of every single file in the repo. If a file is modified, then the committed version is generated and compared with the current version of your file. It is then the same as diff'ing two files on the hard drive. If the diff tool can diff two ordinary files, then it can diff the version that git produced and the version that you have.

Unless if there is some really obscure bug, the diff tool should be able to catch any difference, as the diff tool compares the two files line by line.