Mathematica is a product that uses the Wolfram Language. As will be the Programming Cloud.
"Mathematica in the cloud" would be Mathematica Online, a separate product from the Programming Cloud: http://www.wolfram.com/mathematica/online/
See http://www.wolframcloud.com/ for a wider overview.
The Programming Cloud is specifically focused around workflows and features that programmers are likely to want and need.
So I doubt any of us would have told you that the Programming Cloud is "Mathematica running on our servers with better data store and NLP integration." That's not the way we think or talk internally about our technology stack, and its certainly not the way we talk to customers.