I have the registered version of Tg3 for pc. Do I have to purchase again for my mac?
You can move it to your mac, but hen it cant be on your PC. IF you have it on two systems, then you need two keys. If you only want it on your mac, download the OSX version, and uninstall the PC version.
However, if you have a license that allows you more render nodes. Then that means you can have TG on as many systems as you have nodes in your license. Not sure if you use the same key for that or if you get a key for each one.
Badger is essentially correct. With render nodes, you use the same key for multiple installations.