There are 100,000 Minke whales in existence. The Japanese kill about 500 per year. They take much smaller numbers--less than a hundred--Sei, Fin and Brydes whales, all of which also have populations of at least 50,000.
They also take a handful of Sperm whales, who number at least a quarter million and perhaps many more. The Sperm whale is called a whale only because of historical tradition and its huge size. It is actually a "toothed whale" and is technically a member of the clade of dolphins, all of which are toothed whales. All other animals called whales are "baleen whales" who eat by sifting krill through their baleen plates: basically grazing on tiny shrimp rather than hunting prey like dolphins and Sperm whales. The only other exception is the orca, a large dolphin formerly referred to as the "killer whale."
The Japanese have been eating whale meat since the Jomon period, the Neolithic Era or Late Stone Age in Japan which ended during the first millennium BCE.
The town of Taiji on Honshu is where Japan's modern whaling methods were developed, and dolphins are still hunted and eaten there.