> Wouldn't the interface in C simply be called function headers? Why are we using the term API? It seems a word like "function signatures" would also make it clear (or just signatures or headers).

First, to contrast the "application programmer interface" (i.e. what code has to be written to use it properly in an environment with a compiler) from the "application binary interface" (i.e. what actual bytes have to be provided in order to work with an already compiled version — important for linking, inter-process communication etc.).

Second, to be able to talk about what you actually do with the headers (i.e. what the rules are for using the code) separately from the headers themselves (i.e. just the code itself), and to abstract over other programming languages that don't work the same way.

> They're roles, not distinct hardware.

So, you already understand the value of these kinds of distinctions. A shame we haven't historically made them more consistently. (As an exercise, try to list everything that "static" can mean in every programming language you know where that's a keyword. For bonus points, contrast and compare to how the word is used in the discussion of programming language design.)

> Maybe I just don't understand what the word interface means other than the GUI version of it. What's an interface in the analogue world? ... Claude mentions:

In the world that I was recalling, when people were unfamiliar with a word, they used a resource called a "dictionary" to look them up. This provided a pre-written answer directly, rather than relying on sophisticated computer models to come up with something new every time. Admittedly, this did trend towards online use over time, in particular since this made it easier to update these resources to reflect current use patterns. But those online resources are still available, e.g. https://www.merriam-webster.com/dictionary/interface .

Even with AI expanding so far as to creep into search engines, you can still reliably obtain such definitions with search queries consisting of "define" + the word.