The conda binaries and pip wheels will use their own CUDA runtime (which you specify during the installation) as well as cudnn, NCCL etc., so your local CUDA toolkit won’t be used.
The local CUDA toolkit (and in particular the compiler) will be used if you are building a custom CUDA extension or PyTorch from source.
Are both machines using the same PyTorch, CUDA, cudnn installation (e.g. through conda) as well as the same GPU?
If so, are both GPUs free before you start the training or is e.g. Windows using it to display the desktop (which will use GPU memory)?