Good question - it can be very confusing!
The liquid that comes out of the coconut is coconut water. It is highly refreshing and makes a great drink in hot humid conditions.
Coconut "milk" is made by blending the coconut flesh with water. A good brand should just have coconut and water in the ingredients though sometimes you do see something else added to keep them blended together, or homogenised, as otherwise the coconut tends to settle at the bottom of the container!
I haven't encountered coconut cream but I would think it is the same as the milk but with a higher proportion of coconut to water. Or maybe just the coconut flesh but blitzed until it becomes smooth and creamy.