Yes - cream of coconut milk is usually very sweet and used to make cocktails. Usually the label depicts a drink with an elaborate garnish involving multiple types of fruit and a few umbrellas.

Coconut milk is unsweetened. You can't sub cream of coconut milk for coconut milk, unless perhaps you're making dessert - in which case watch the sugar in the recipe.

There is also a product called "coconut cream" that is available in Asian grocery stores, which is a thicker version of coconut milk and great for Thai curries, or can be diluted to make coconut milk. Unsweetened coconut cream is hard to find in western grocery stores, in my experience.

Yes! There's a huge difference. Cream of Coconut is incredibly sweet and typically used to make pina coladas. Coconut milk is barely sweet (just the natural sweetness of coconut).