Other way around. The fish in the first photo is Melichthys indicus, Black Durgeon, aka Indian Trigger (I prefer this name). The second fish you posted is Melichthys niger the Hawaiian Black. SWF does indeed have it wrong.
You were right though, the difference is in the shape of the tail. Niger has the crescent shape, while the indicus has the more simple tail fin. However Indicus is probably the better buy. Hawaiians are quite rare to get small, and grow to a very large size. Indian's are more commonly available and stay more manageably sized. They both are quite active fish and hope you have a larger tank. Personally, I wouldn't stick one in my 125gal.