i think water is just the water inside and not the flesh/pulp. juice is when its pressed/squashed like an orange and the liquid is collected. plant milks are generally when the plant is blended and filtered through something like a cheese cloth.
when you open a coconut inside it will contain a liquid that is coconut water, when you press the green (immature) coconut husk you will get the juice and when you beat the pulp with water the milk, if you use a little water it will become thicker and when letting it rest on the surface, it will form a layer of coconut cream that is nothing more than coconut oil with “impurities” that is, there is coconut milk in the oil