I can't wait for the day when the differences between x64 and x86 will become common knowledge. That will probably be around the time we are running a 128-bit version of Windows.
You have two separate Program Files directories, by design, to keep the x86 native apps separate from the x64 native apps. it is perfectly normal, and when you are installing something, let it go to the directory it chooses.
You also obviously have a 64-bit capable processor, or else you wouldn't be running Windows 7 x64. For future reference, fill out your system specs, and then we'd know for sure what processor you had.