That's the library/framework API that you are talking about (API also meant something else before it referred to e.g. a REST API).
So it's just the API or API code? Just feels weird to say that about syntax. It might be because so many think of something else with the term, it seems out of place.
Yes, that'll also depend on who you're talking to/with. Do note though, that you'll not come across many people who'd refer to it as a 'language' rather than a library or framework, since 'language' has a pretty widespread specific meaning in IT.
The short answer here is: it's just "the library API" or "the library's API'.
Something to keep in mind in that the 'i' in API stands for interface. So the code you write is meant to (i.e. is your way to) interface with the library or framework. Code is just statements, written in whatever language. So saying 'API code' is equivalent to saying 'looping code', while just calling it 'a loop' works just fine.
I think you'd be surprised how many people do use the term 'API' in the sense that I'm talking about, rather than only in the http/REST/SOAP sense. The following might offer some help: quora.com/What-is-the-difference-b.... Most notably: "An API is an interface for other programs to interact with your program or library without having direct access."
To give a very quick but telling example, have a look at api.jquery.com/ and it's subpages. The 'api' there has nothing whatsoever to do with ajax calls to json http APIs, but in fact refers to the library's (or libraries') surface area, with which you can interact and make use of.
This isn't different then writing a C library with library specific macros, enums, and typedefs. The code you write with it could look very different, but it is still C.
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