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.