Mathematica[0] and The Wolfram Language[1] are two different things. The Wolfram Language is a sort of extension of their Wolfram Alpha service, which Wolfram itself describes as "Knowledge Based." Mathematica is still just Mathematica.
I'm not great at following markitecture, but didn't Mathematica exist and have a language before this language was rebraded as the Wolfram Language? There is nothing really wrong with this, but its understandable that people might be confused about it right now.
That's right, and what seems to be confusing people is that the language underlying Mathematica-the-product was always, implicitly, "Mathematica".
We were a one-product company, and it didn't make sense to distinguish Mathematica-the-product and the language it ran.
The last time we'd tried to branch the underlying language off into its own thing was in the early nineties, where a certain intern by the name of Brin was in the middle of refactoring the code before he went off to do other things :).
My prediction is that the confusion will pass soon once we have these concrete products actually out in the world.
A new generation of people will be using and seeing the language for the first time. And they'll be doing stuff that old-school Mathematica-the-product (and most of its user base) would find quite alien.
Things like trying code out in online sandboxes, coding things in the cloud IDE (or locally, via Eclipse or "Wolfram Desktop"), deploying public APIs for other people to use, building websites totally within the language, doing internet-of-things type stuff, embedding chunks of WL code in Java or Python or whatever, writing natural language parsers on top of Alpha's technology, creating data science workflows, making private clouds, designing interactive visualizations, tweeting code at our executor-bot... and on and on...
Mathematica is a commercial piece of desktop software that uses the Wolfram Language. Just like how RStudio uses R.
There are other product platforms (coming soon) that employ the Wolfram Language, both in cloud and desktop incarnations: http://www.wolframcloud.com/