I'm not sure about "science," but: According to the OED, the noun form of "skill" and the obsolete English verb "skill" (to separate, from Old Norse skilja) are

I'm not sure about "science," but: According to the OED, the noun form of "skill" and the obsolete English verb "skill" (to separate, from Old Norse skilja) are both related to earlier Germanic words for distinction/difference. However, in Middle English, the meaning of skill varied a great deal, sometimes representing, for example: "a statement made by way of argument or reasoning."