I think you're right, this is probably the BSD equivalent of Cygwin.
That being said... I feel the distinction is very blurred, and even more so with the inclusion of MSYS. It seems very few people use naked MinGW, despite a few distributions[1][2] being available.
For instance, MinGW also provides `unistd.h` and `pthread.h` on top of `windows.h`. Certain distributions of MinGW provide lib{std}c++ instead of MSVC STL. Where does 'build native Windows executables from source files that are already targetted at Windows' stop, and 'allows compiling source code intended for *nix to native Windows binaries' begin?
Also, based on my comment above, MinGW doesn't do a great job at 'already targetted at Windows', because some very core libraries that rely on fundamental Windows-y constructs don't work. Personally I avoid it because of its incompleteness, and just use straight `clang++.exe` from the Windows LLVM release[4], aside a full install of the Windows and MSVC SDKs.
[1]: https://github.com/skeeto/w64devkit
[2]: https://github.com/mstorsjo/llvm-mingw
[3]: https://github.com/llvm/llvm-project/releases/download/llvmo...