The confusion here is because Pest is not, in fact, a parser. It's a parser generator: you can use it to generate parsers (maybe even a parser for Rust), but it is not in itself a parser.

A better title would be "Pest - Fast, modern parser generator for Rust".

One cool thing is that rather than the parser generation being a standalone tool, it's written using Rust's macro system. Normal parser generators use some sort of command line tool to generate say C code which can then be used like any other library. Here, there's no need for generated code, because the Rust macro system generates it on the fly.