BlitzMax is the new, next generation game programming language from Blitz Research. BlitzMax retains the BASIC roots of Blitz3D and BlitzPlus, but adds a ton of cool new features and abilities.
Mingw is the collection of C/C++ compilers and tools used to build BlitzMax on Windows.
You only need to install Mingw if you plan to rebuild Blitz Research or third party modules. BlitzMax can be used 'as is' to create applications without having to install Mingw.