You don't need to buy a second version. Your license agreement allows you to use your license key on two machines. One limitation is that you won't be able to connect to a shared database with both machines at the same time.
You will need a separate installer for the Mac, which you can from the original download link if you've purchased it recently (30 or 90 days I think before the link expires). Otherwise, you'll need to contact Filemaker for a new link, or, if you're using Filemaker Pro, not Advanced, download the trial version and perform a minor hack.
Wow I wish I knew that. I just upgraded my Advanced, so I have two MACs running Parrellel on bot. So I will use the extra license for one machine for both Windows and MAC and then I will buy another for my other computer. Thank you for the advice you just saved me about 500 bucks.