No, you’re misunderstanding. There is no 1⁄2 cup of butter anywhere in the above scenario. One stick of butter is 4 oz. of butter (weight), but not 1⁄2 cup of butter (volume).
But 1⁄2 cup of butter weighs 4 ounces according to every source I can find: https://www.wolframalpha.com/input?i=density+of+butter+*+(1%2F2+cup)+in+ounces
Which means a 4 ounce stick of butter is 1⁄2 cup by volume.
No, you’re misunderstanding. There is no 1⁄2 cup of butter anywhere in the above scenario. One stick of butter is 4 oz. of butter (weight), but not 1⁄2 cup of butter (volume).
But 1⁄2 cup of butter weighs 4 ounces according to every source I can find: https://www.wolframalpha.com/input?i=density+of+butter+*+(1%2F2+cup)+in+ounces
Which means a 4 ounce stick of butter is 1⁄2 cup by volume.