Coastal Indian vegetarian cooking builds rich gravies without cream by using coconut in several forms. Each form behaves differently, and confusing them is the usual cause of a failed dish.
Fresh grated coconut thickens by bulk
Ground with water and spices, grated coconut becomes a paste of fine solids suspended in liquid. Those solids give the gravy body the way a nut paste does.
The coconut also brings fat and a distinct sweetness, so it is never a neutral thickener. A gravy built on it tastes of coconut regardless of what else is in it.
Grinding finely matters, because coarse fragments read as texture in the mouth rather than dissolving into a smooth sauce.
Coconut milk is an emulsion, not a liquid
Coconut milk is fat suspended in water, held there by proteins and by the physical structure created when the flesh is pressed. It behaves like dairy cream in this respect.
Emulsions break under sustained boiling, because the fat coalesces and separates out as an oily layer. This is the split that ruins a coconut curry.
The fix is the same as with dairy, which is to add it late, keep the pot below a rolling boil, and stir rather than leave it undisturbed.
Coconut oil is the third form
In several coastal regions the cooking fat itself is coconut oil, which carries a pronounced aroma and reinforces the flavor already coming from the flesh and the milk.
It solidifies below normal room temperature in a cool kitchen, which surprises cooks in northern American winters and means a jar may need warming before it will pour.
Refined and unrefined versions taste entirely different. The refined product is close to neutral, so a recipe assuming the aroma will fall flat if the refined one is used.
Acid and coconut have to be managed
Tamarind and raw mango appear constantly alongside coconut in coastal cooking, and acid destabilizes emulsions, which makes the order of addition consequential.
Cooks usually establish the sour element in the base and finish with the thickest coconut extract off the heat, which keeps the fat where it belongs.
Salt behaves the same way, since a heavily salted liquid also stresses the emulsion, which is why seasoning is adjusted before the final extract rather than after it.
Canned and fresh are not equivalent
Canned coconut milk is standardized and often carries stabilizers, which makes it more forgiving of heat than a fresh extract pressed at home.
Fresh extraction yields a thick first press and a thinner second, and traditional recipes use the thin one for cooking and reserve the thick one for finishing.
Frozen grated coconut sold in Indian groceries is the closest widely available substitute for fresh, and it grinds into a paste better than dried desiccated coconut ever will.