The names coco betaine and cocamidopropyl betaine are often used interchangeably but they aren't exactly the same.
Coco betaine is a natural surfactant used in all of the products mentioned above. The “coco” refers to coconut oil. Betaine is a naturally-derived ingredient used to thicken and improve the texture of certain products. It also helps to hydrate skin and smooth hair.
Cocamidopropyl betaine has a slightly-different chemical. Like all surfactants, both substances are created through a synthetic process (but used in similar applications to achieve the same results).