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Saiyans were originally giant monkeys with pointy demon ears. They came from the demon realm. Then one day the prince of the Ozaru became sentient and wished his people could become smart and get along with the other races. The Dragon God, Zalama, heard this wish and used the Super Dragon Balls to make all saiyans across all universes into humanoids, but allowed them to retain their ancestral form until they were each individually ready to get rid of it. The U6 saiyans did not desire this ancestral form, hence why they lost their tails.
Saiyan humanoids are based on the ancestors of the humans, who once dominated the universe but died out and lost contact with one another, becoming many different races. The saiyan prince fell in love with a human woman, which is also why he wished to be like us.