32-bit versus 64-bit
I have a PC running 32-bit Windows XP Pro. It has a 64-bit processor, but after upgrading, I found the 32-bit version installed.
As you discovered, the Windows download from Microsoft matches the system from which you initiate the download. So if you purchase the download on a system running 32-bit Windows, your downloaded setup file will also be 32-bit.
But there’s an easy (and legal) way to get a 64-bit downloader, as long as you have access to a PC running any 64-bit version of Windows (including Windows 8).
After you complete the purchase, you will receive an email confirmation that includes a product key and a download link. From a 64-bit PC, click that download link and enter the product key you received. The download will commence, and when it finishes, you will have a 64-bit Windows installer that you can save as an ISO or burn to bootable media.
How do I get to 64 bit from 32 bit Windows?
There is no way to upgrade from a 32-bit copy of Windows to 64-bit, or vice versa. You must backup your data, create bootable media, and do a clean install. After you’re done, you’ll need to reinstall your programs and restore your data.