marco_c:
It is a subset C++ with library extensions that simplify access to hardware functionality. Not all the 'standard' C++ libraries make sense in the Arduino environment as there is very limited flash memory and RAM.
You can also use straight C if you want and it works as well, or in fact not use the hardware access extensions at all.
I would say that 'Arduino' refers to a development environment (hardware and software) that is based on C++ that simplifies the creation of portable code for devices that support the ecosystem.It is designed to lower the entry barriers for beginners at the expense of some speed or efficiency.
This is a detailed answer but I believe it is mistaken. You write "it is a subset [of] C++ with library extensions" but in fact it should be full, standard C++ (the language) - not in any way or sense a subset. Of course, you cannot compile Firefox with it, even though Firefox is written in C++, but not because Arduino is a "subset of C++" (the language) but rather because the compiler target is a microcontroller with the limitations that you've specified.
Here I am asking about C++ the language, rather than C++ the development environment.
As such, if I would like an alternative set of tools to translate a Sketch (in the arduino [templating] language' into a compiled program, other than using the default Arduino IDE, then I could do so if I followed the same standard.
It sounds like from your answer that there is no such standard. I could only just make a work-alike. But that the Arduino IDE could change its behavior slightly in future versions.
[This question had errors and I'm removing it after complaints.]