Firstly, I have noticed all the curried dishes we eat in an Indian restaurant feel "creamy".
Now, I don't know whether they add cream, or yogurt, or coconut milk?
In which kinds of dishes do we need which kind of substance to make it creamy?
Rule of thumb, dairy in the north and coconut in southern recipes. ie korma wouldn't have coconut
Indian yogurt is made with whole milk. As with western recipes, balancing the fat for good mouth-feel is important: yogurt can be a good choice when a larger quantity of liquid is called for. Cream works great when a finishing splash smooths out flavors without watering down
Acidity is also important. Does the dish need a tangy component or a softening of acids? A dish could use both: yogurt marinade then a bit of cream to finish.
For richness and a hint of sweetness along with a wonderful aroma, coconut can't be beat but will be a discernable flavor in most curries. Many restaurants are making use of coconut where it is less than traditional with good results.
Well, first I would like to answer this questions in two ways: when we add substances to make the cuisine creamy, and what to be added when cuisine is prepared.
When we add substance to make cuisine creamy:
While preparing North Indian/South Indian dishes (like kurma and other items) we used to add the coconut milk while the specific dish gets boiled. Usually coconut milk will be mixed with yeast.
What kind of substance to make cuisine creamy:
For liquid food items (e.g kurma) add the coconut milk with little yeast, and for dishes like biryani add the coconut oil with spicy items to make the cuisine better.
The creamy texture for Indian dishes like Shahi Paneer, Chicken Mughlai etc can be arrived by adding pureed nuts like cashews and almonds to these dishes.
Firstly, an awful lot depends on exactly what you mean by the term 'creamy'. Can you be more specific about what you mean by this term?
Secondly, you mention 'Indian Restaurants', but you don't say where these restaurants are located, are you referring to ones located in India? Geographically, Indian restaurants will vary, depending on where they're located.
Thirdly, is there a specific dish you're referring to here?
Ideally, I need clarification on those points before I can answer your question, but from my own interpretation of what you mean it has nothing to do with cream, yogurt or coconut milk.
As Pat Sommer rightly points out, the smooth 'creamy' like texture you find prevalent in many if not all India Restaurant dishes is a result of 'base sauce' of pureed onions and other ingredients.
Pretty much all commercial Indian restaurants will use some form of 'base sauce or gravy' as the basis for most of their dishes. To this are added other specific ingredients specific to the dish. Some restaurants will have more than one base sauce some will add pureed lentils etc., but the base sauce itself it's predominantly made from fried and simmered onions, garlic, ginger, tomatoes and spices, water and then pureed.
It's this 'base sauce' I believe you're referring to which is giving the 'creamy' texture to the dish you refer to in your question.