OME Version

Whatever is on that CD, the key will dictate what you could install and what you can't. If you ain't given no choices during install, than you got what the key is purchased for.

The way I understand it is the key will work on either 32bit or 64bit of the same version, Home Premium for example.

Looks like OEMs are sending one or the other and not two DVDs, 32bit and 64bit.
Unless, like someone said, both 32bit and 64 bit are both on one DVD, haven't heard this before.

So to answer the OP question, yes you can use someone else's DVD if it's the same version except 64bit, then use your key.

When you buy the Retail Upgrade version, you get one 32bit DVD and one 64bit DVD and one key.

Your key is good for one installation of MS Windows OS.
You can decide which one you want to install, 32bit or 64bit.

Some OEMs send you only one DVD, if you don't specify they send 32bit.

Your Key will work, lets say you bought an Upgrade version of Home Premium, you can upgrade from Vista to Win7, pick 32bit or 64bit, the key will work.
As long as your friends OEM upgrade is from the same OEM as yours, it will work.

For well over a year MS and most OEMs will send you a 64bit equivalent version of MS Windows, if you have Vista Home Premium 32bit they will send you Vista Home Premium 64bit, for free or shipping costs. You install the 64bit OS using the same 32bit key that you already have. Most OEM manufacturers Windows OS don't require you to enter a key, it's done automatically.