What is the difference between Android Beam on the Galaxy Nexus and S Beam on Galaxy S3?
Are these two features inter-compatible? Can I transfer data between the two devices?
Even though Android Beam and S Beam serve similar purposes, they actually work very differently and are not compatible with one another.
Android Beam uses NFC to pair your devices over Bluetooth, then transfers files over the Bluetooth connection. I believe it can also transfer very small pieces of data (contacts, links, etc) directly over NFC, as the Ice Cream Sandwich version highlights page implies:
S Beam, however, uses Wi-Fi Direct to perform data transfers instead of Bluetooth. Their reasoning for doing this is that Wi-Fi Direct offers faster transfer speeds (they quote up to 300 Mbps). Therefore, this will only work with other S Beam enabled devices, currently limiting it to communication between two Galaxy S3s.
However, the SGS3 also supports Android Beam, so you can use that to transfer something between a GNex and an SGS3. Here is a tutorial on Sprint's website (should be essentially the same for other versions of the SGS3).