Watson refers to the technologies used in the Jeopardy system, yes. Specifically, it refers to the Watson API, which consists of all the NLP and AI algorithms used in the Jeopardy system repackaged (with additions) and hidden under a simpler, query-based system. The Watson API is becoming the basis for most of IBM's Bluemix services which are described by IBM as "cognitive" (as you phrase it, "semi-intelligent systems" - referring mainly to NLP and related applications).

IBM is working on a number of applications to use the Watson API, as well as inviting other developers to use the API. Watson Analytics is just one of these applications, but it doesn't run on Watson alone. It is probably better to think of these applications as fitting within the overall framework of IBM's bluemix services, which includes Watson but also other technologies less geared towards NLP.

https://console.ng.bluemix.net/

Yeah, this appears to be just online statistics. The only "AI" thing about it is that it can match natural language queries to your spreadsheet column names.