As everyone says, you can use the same key. If you buy a retail copy, you get 1 key and 2 DVDs (1 64-bit and the other is 32-bit). You can install whichever. Same logic applies to a non retail version.
There's nothing like a "32-bit key" or anything. keys are not tied to individual DVDs, they're decrypted (sort of) to get a specific result that should be valid (this is done by the software during installation). Install source doesn't matter. Microsoft's database sort of ties the key to your MAC address i suppose, so you can reinstall on the same computer as many times as you want (this is why they validate the key).
Now i'm not sure what i'm saying 100% accurate in the way it's done, but it's how i understand it to work. Regardless, you can use your key without a prob
Forgot to mention that this key is specific to a particular version of Windows, so it'll work on Windows 7 HP only. That key's decrypted result is different for different versions. So basically if you use "windows anytime upgrade" and buy a key for win 7 pro, then all windows does is verify the key and unlock more features. May ask you for the dvd to install new features (never tried personally, may be wrong), but that's the process (roughly).