MinGW-w32 vs. MinGW

The MinGW from http://www.mingw.org/ does only support gcc 32 bit (host and target). The independent minGW-w64 project provides support for 64 bit, and also supports a much larger part of the Windows API. The MinGW-w64 project however does not provide official binary builds: These can be grabbed either from the personal build directories of the developers (the most popular being rubenvb), or from associated but independent projects like tdm-gcc or mingw-builds or msys2.

Source: http://wiki.qt.io/MinGW-64-bit

There's a bit of insight into this in the Wikipedia talk page on the MinGW article. Basically, it appears that the MinGW-w64 project is a fork of the MinGW source base. I have found very little clear information on the details of why the fork happened (although this mailing-list post and this rebuttalimplies it was some form of the usual sort of open-source politics), or of the subsequent differences between the two projects.

To a first approximation, they're the same; the differences will come in in subsequent development.

One looks like it "cross compiles", from 64 bit to 32 bit, whereas the other looks native.

That was just a quick look though, so I could be a long long way off the mark here......

EDIT: This is only somewhat true. A better explanation is provided here

As said by others MinGW-w64 is a fork of the original MinGW which supports both 32 and 64bit x86 processors. You can find the original motivation for the fork here:

https://sourceforge.net/p/mingw-w64/wiki2/History/

Regarding the differences you can find a list here:

https://sourceforge.net/p/mingw-w64/wiki2/Feature%20list/