It is a little misleading that there are two animals with common names suggesting a close relationship sperm whales: the dwarf sperm whale, and the pygmy sperm whale. Such terms, more often than not, are applied to distinguish two species in the same genus (for comparison, the human equivalent would be hominids such as Peking Man). These other two species are not even in its family (humans are in the great ape family), and it is currently not even certain they belong to the same superfamily (for us that equivalent is the apes).
The existence of animals called dwarf and pygmy sperm whales has led a small number of sources to refer to sperm whales as giant sperm whales. I believe this to be confusing, and that term better reserved for fully mature males of the species.
Sperm whales are today the only member or their family. Contrast that with the killer whales, who have at least thirty other whales and dolphins in their own family. This solitary status has been brought about by a rapid collapse from a rather large group. Exactly how diverse, and how sudden that collapse is very hard to say, due to the poor and fragmentary nature of their fossil record.
Sometimes, biological success is equated with species diversity, but it is hard to conclude that here when the sperm whales have 15 – 100 times the biomass of the killer whale species. In fact, by the most probable figures listed in Wikipedia, they have at least five times the biomass of every species combined in the diverse family to which the killer whale belongs.