How is Scoop different from Cygwin and MSYS?
The most concise description of 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 description, 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.