Coconut milk is made by pureeing a mixture of coconut meat and water, then straining it to remove some of the fat. A second straining will yield a lower fat coconut milk. Coconut cream is made in the same way as coconut milk, but it is made with a higher ratio of coconut to water. Sometimes, coconut cream will form on the top of canned coconut milk. The two are pretty much interchangeable in recipes, though they have slightly different consistencies. For the curious, some other drinks, such as almond milk, are made in the same way.
Cream of coconut is not the same as coconut cream. It is the creamy liquid often added to pina coladas (and various other drinks and dishes). Though it starts out as coconut cream, sugars and stabilizers are added to give it an especially creamy consistency and to make it more palate-pleasing in drinks and desserts.