It seems to me that Watson is basically just IBM's version of AWS/GCE services (at least the non infra ones). But it gets thrown around as a buzzword so often. The marketing makes it look like there's a single AI codebase that can be accessed through a bunch of APIs, but I would be very surprised if that was actually the case.
Both, sort of. There is a "thing" called Watson, which is related to the Watson that played Jeopardy. But "Watson" is also a brand which lumps in stuff that has absolutely nothing to do with the "old" Watson.
To illustrate a bit.. "Watson Health" is (or was) made up of a ton of people and technologies who came into IBM as the result of several acquisitions: Truven, Phytel, Explorys, etc. In many cases, they repackaged stuff from those vendors, gave it a "Watson name" and shipped it. And some of this stuff was literally no more sophisticated than linear regression / logistic regression, etc.
https://news.ycombinator.com/item?id=15456211
It's reasonably in depth and appears sincere.
tl;dr: it's a good search engine and a disparate set of machine learning tools. Sales is promising Hollywood AI, but the reality is that it takes a sizable project team to build anything worthwhile.
Scanning past commentary, it seems that startups are eating their lunch (more nimble, dedicated to customer space). I'll add that half the machine learning battle is getting access to data, so hyping the brand makes sense strategically.