Read your canned coconut milk label!
Whenever I see coconut milk on sale, I stock up a few cans, regardless of the brand, thinking that they should be fairly similar.
So I pull out one can each of two different brands, since the recipe for Coconut Rice Pudding called for 2 cups and each can is 13.5 oz. Upon opening them, I discovered the thickness of one brand was like that of creme fraiche while the other brand was much more like coconut milk; a somewhat watered down whole milk. Reading the labels, which is what I should've done before buying, I found that the thick coconut milk was coconut extract, water, and "thickeners", while the other actually said "coconut milk".
So I mixed the two, and had to alter the cooking time to adjust for the thickness, which is normally obtained through the cooking.
Lesson learned!! Get the real stuff!!
Oh god, oh god, oh god..... KILL yourself now... canned coconut milk/cream is horrendous. DON'T do it.....
Buy a good coconut, get a chinese cleaver and whack the shell while rotating it until it cracks in half and the water released. Rinse the coconut. Then take one of the Sri Lankan/indian coconut scrapers and scrape the coconut out...... then add warm water.... place the immersion blender in it to mix it a little then squeeze out the coconut milk cream goodness through a cheesecloth.... The cream will rise to the top, the milk on the bottom. The 15 minutes it will take you to make your own - will be the best 15 minutes you can invest. Canned is crap.
Believe this version was invented in Sri Lanka 50+ years ago, also available in Indian specialty stores - if you have Sri Lankan friends they might show you where it can be had.
This is not the best brand - but it is good enough - I just get many of them for when they wear out.
Frozen is better than canned (taste wise) but it does change the texture a little.
I've heard tetra pak coconut milk is pretty good as it doesn't have any additives. Never tried it as I end up making my own using dessicated coconut as it's fresher and cheaper. I guess you can make a whole bunch and put it in the freezer for later consumption if you wish.