What are the differences between Coconut Milk, Coconut Water, and Coconut Oil?
Coconut milk:


  is an opaque, milky-white liquid extracted from the grated pulp of mature coconuts.


Coconut water:


  is the clear liquid inside coconuts.


Coconut water is typically extracted from younger coconuts. The milk contains both coconut water and ground-up coconut flesh.

Cocunut oil:


  is an edible oil extracted from the kernel or meat of mature coconuts harvested from the coconut palm.


So, the milk also contains some coconut oil.

There will be little to no coconut oil in coconut water. The question "is there milk in the oil?" makes little sense given the above, as the oil is one of the components of the milk. This is like asking if there is milk in milk fats.