You raise a really important distinction considering the increasing number of initiatives advocating for kids learning to code. Coding is a rather small part of computer science and of the actual process of writing a program (as also pointed out LAKristopher). I totally agree with you that what is important is not the actual code but the thought processes that go before writing the code; the analysis, problem solving and structured thinking you have to go through in order to be able to tell someone (or something) how you went about sorting the numbers. Still, I do think that the example you give for the coding part is too simplified. Sure, no one expects a programmer to write their own implementations for sorting and other functions needed on a regular basis. But I cannot think of anyone teaching an introductory course in programming, who would let students use ready-made functions without first having implemented it themselves (that is, formalizing the idea/algorithm you describe in the "What is CS"-part).
When discussing what should and should not be covered at lower levels of education, I prefer to talk about computational thinking instead of programming, coding or even computer science. To me Wing's idea of computational thinking, describing a toolbox of thinking skills related to computer science that everyone can benefit from regardless of their own discipline, feels like a more "neutral" and more widely applicable term than any of the more traditional ones.