Coconut milk in most countries is the same consistency as dairy milk and contains added water. In the USA some brands call themselves coconut milk but are actually what other countries would call cocconut cream. Most curries use coconut cream rather than coconut milk, which contains no/less added water. I think what you are describing is coconut cream, or you are from the USA and use something called coconut milk but its actually quite thicker than what some others think of as coconut milk.