I'm not entirely sure, but I think the difference between coconut milk and coconut cream is similar to cow's milk and cream - the cream is... well... creamier. However, I've found that the milk has a more coconut-y taste, while cream just tastes richer. I've experimented with substituting cream for milk in Thai curries, and as you'd expect, the cream makes the sauce thicker and richer than the milk. Personally, I prefer the stronger coconut taste, so I try to use milk.
Hope that helps!