No, it is not a computer algebra system, not a symbolic computation system, not a computational mathematics system, not a technical computing system, not a development system, not a HPC system, not a family of solutions, not the implementation system for Wolfram|Alpha, ... It is much more, but what?
Mathematica is the world's ultimate application for computations and the only development platform fully integrating computation into complete workflows, moving you seamlessly from initial ideas all the way to deployed individual or enterprise solutions, says Wolfram.
As UnRisk and mlf developers, we use Mathematica intensively, exploit many of its features and capabilities and transform them into systems that are solutions and development systems in one. We provide domain specific programming in the language of Mathematica, we extend the Mathematica kernel with our blazingly fast engines and solvers seamlessly? We exploit its symbolic parallelization and drive OpenCL over gridMathematica, ...
It seems, it is simply MORE than a name can embrace? This has also a little downside - it is not so easy to position?