If you look at the file lists on the Ubuntu package webserver for mingw-w64‘s constituent packages:
gcc-mingw-w64-x86-64g++-mingw-w64-x86-64binutils-mingw-w64-x86-64mingw-w64-x86-64-devgcc-mingw-w64-i686g++-mingw-w64-i686binutils-mingw-w64-i686mingw-w64-i686-dev
You can see that mingw-w64 provides a toolchain, i.e. a set of alternative tools (compiler, linker, headers, etc.) used to compile your code for another system.
Assuming you want to compile C++ code for a 64-bit system, you’ll need to use /usr/bin/x86_64-w64-mingw32-g++-win32. You can use the CXX environment variable to tell most Makefiles to use that compiler to compile code.