The case that makes local processing matter
The texts genuinely worth comparing tend to be the ones you should not paste into a random website: two versions of a contract, a config file holding credentials, an API response carrying customer data. Here the comparison executes in your tab, so that content never leaves your machine.
Line-by-line comparison
The tool aligns both texts and marks which lines were added, which disappeared and which stayed put. It is the same mental model as a version-control `diff`, with nothing to install and no requirement that the text be code.
When the result is full of differences that are not real
It is almost always line endings. A file saved on Windows ends each line with CRLF, one from macOS or Linux with LF; to a comparison those are different lines even though they look identical on screen. Trailing whitespace and tabs versus spaces do the same thing. If every line shows as changed, start there.