Whirlfloc contains purified high molecular weight carrageenan from algae. Irish Moss also contains carrageenan just it has not been purified to the same extent and therefore probably isn't quite as effective. Brewbrite also contains purified carrageenan but also PVPP.
Irish moss is the raw material
Whirlfloc is made up of selected high molecular weight carrageenan's extracted from Irish Moss and a dispersant (the part that makes it whirl) it moves around on the surface of the boiling wort to better disperse the carrageenan through the wort.
BrewBright is Kappa-Carrageenan (the most effective of the many carrageenan's found in Irish Moss and some other seaweeds) and PVPP that chemically binds polyphenols, the removal of high molecular weight proteins by Carrageenan and reduction in wort polyphenols (the other half of the haze forming equation) works better, in my experience, than does either Whirlfloc, and certainly much better than Irish Moss alone.
Mark
I think (and I could be wrong here) that whirlfloc tablets contain Irish moss, while brewbrite contains Irish moss and PVPP which helps with chill haze.
If I'm wrong hopefully somebody will correct me.
EDIT: obviously people are faster typists than me, and also know far more about finings.