What program are we coding in?

Sorry! Wasn't sure where exactly to put this rather general question..

But there are tons of C++ based languages out there that aren't.. "C++." The higher level C++ languages have their own names. like "R" for instance. But for the arduino, does the language have its own name?

There is nothing like 'Arduino language'.

It is just plain C++, spiced with some libraries and an 'easy framework' mechanism.

The IDE supplies the standard C++ main(), that calls setup(), loop() and some other functions.

But as the Arduino is open source, you can look under the hood. ;)