GCC does not include a C runtime library. This is supplied by the platform. The MinGW port of GCC uses Microsoft's original (old) Visual C runtime, MSVCRT, which was targeted by Microsoft Visual Studio 6 (released in 1998).
The Cygwin project was started in 1995 by Steve Chamberlain to allow GNU tools to be used on Windows.
MinGW ("Minimalistic GNU for Windows") is a collection of freely available and freely distributable Windows specific header files and import libraries combined with GNU toolsets that allow one to produce native Windows programs that do not rely on any 3rd-party C runtime DLLs.
MSYS is a collection of GNU utilities such as bash, make, gawk and grep to allow building of applications and programs which depend on traditionally UNIX tools to be present. It is intended to supplement MinGW and the deficiencies of the cmd shell.
An example would be building a library that uses the autotools build system. Users will typically run "./configure" then "make" to build it. The configure shell script requires a shell script interpreter which is not present on Windows systems, but provided by MSYS.