Coconut Oil vs. Coconut Milk?

Is there any significant difference betweeen the antioxidants/fat from coconut oil vs. milk vs. actual coconut?

The cans of coconut milk seem to be a lot cheaper than the oil, which is a bit pricy, so I’ve been using about 3oz. of the milk in my shakes. I don’t care about taste, I enjoy all coconut in general and have heard only good things on here about cooking with the oil.

Any thoughts…
Thanks,