How is Scoop different to Cygwin and MSYS?

The most concise comparison I've come across for these 2 projects is an answer by Mike Zick in this thread.

Cygwin is an operating system wrapper
The goal of Cygwin is to provide a Linux Programming API.

Msys is a command shell substitute
The goal of Msys is to provide a POSIX scripting environment.

It's probably not a completely accurate or comprehensive comparison, but it is fairly easy to grasp.

So to parallel this for Scoop:

Scoop is an installer
The goal of Scoop is to let you use Unix-y programs in a normal Windows environment

Using Scoop lets you achieve similar things to Cygwin and MSYS, but without having to learn about and use a separate environment. You can just keep doing what you're already doing but easily access the cross-platform tools you need.

As it happens, a lot of the programs that Scoop installs either come directly from the MinGW/MSYS project, or were built using their tools. Scoop can only hope to achieve its goals because of 15 years of amazing work on MinGW/MSYS, which itself is based on Cygwin.