Puma is a multi-thread, multi-process Rack HTTP server that implements a request buffer.
By comparison, Unicorn (the project upon which Pitchfork is based) is a single-thread, multi-process Rack HTTP server that does not buffer requests, so it's only designed for fast clients (or it needs to be paired with a proxy like Nginx to handle slow clients).
The narrower design of Unicorn results in a simpler, less-flexible potentially more efficient architecture.
The reforking feature that Pitchfork introduces to Unicorn was originally implemented in Puma [1], though they're controlled differently and the underlying implementations are entirely different.
[1] https://github.com/puma/puma/blob/master/5.0-Upgrade.md#fork...