Is coconut milk and coconut juice the same thing?

i want to make Indian rice pudding and one of the ingredients is coconut milk. in the supermarket, i see Coco Lopez in cans, which has sugar mixed with it and is in the drinks section, like it’s for making pina coladas and other drinks. My coworker told me Goya makes coconut milk. Today i look in the Goya section and see Roasted Coconut Juice, which has sugar in it also.

Is coconut juice the same as coconut milk? do you know where i could get unsweetened coconut milk?