mingw: For native build and execution. A lot of Windows IDE's will just work with mingw.
msys2: For posix compatible build but native win32 targets. Useful when your project uses autotools. Like when trying to build someones library. msys2 just tends to work. Trying to get autotools to work under windows tends to exceed my patience, time and brain cells.
cigwin: for a posix compatible build and runtime environment.
Also gcc can be built as a cross compiler. The two times I tried it is was more straight forward that I would have thought.
Note that msys2 isn't just for building programs, it provides a full bash environment with many unix tools and a package manager (pacman, same as in Arch Linux) to install more. The build environment is unixy enough to be able to build more tools from source using the classic ./configure; make; make install route (more or less, may need some modifications in the code).
For me my main use of msys2 is as a shell where i run scripts and command-line utilities with the build stuff being a distant secondary use.
