No, they aren’t. Butter is only one of several components in milk.
Butter is mostly (about 80%) fat. The rest is a small amount of protein and water.
Whole milk, on the other hand, is only about 3.5% fat. Like most drinks, it’s mostly water, but it also contains several different types of protein, minerals, and lactose (a sugar).
To make butter, milk is left to stand until a layer of cream forms on the top; this cream is mostly fat, with a little bit of some of the proteins. The remaining proteins and nearly all of the sugar stay dissolved in the liquid, so butter contains a lot less protein than milk (or than cheese made from milk) and very little sugar.
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