That's how it should be done, the ones with names are just the same ones served everywhere for marketing, like with any cuisine. Boring. Chefs amd cooks constantly create and don't just cook the known ones.
I like the milk much better. The cream is made by simmering coconut flakes in water. Coconut milk is just the water (juice) in the center of the coconut. To make a thicker curry you have to just start your main sauce and cook it down... basically a mother sauce... like when you order Indian... they have the mother sauce and then add individual spices, then meat, then veg. So just cook down the "curry" bare bones portion.