GPU "cores" are basically what a CPU would call SIMD lanes. So a GPU with 1024 'CUDA cores' might be structured as 16 relatively independent pieces that a CPU might call a core, each with a 64 wide SIMD unit.
32 wide - only AMD has a 64 wide mode
64 what? Bits/bytes/something bigger?
32 wide - only AMD has a 64 wide mode