I reject this terminology; I think #2 is superintelligence and #1 is a different dimension.
Also, I would actually differentiate two kinds of #1. There's how much stuff the AI can reason about, which is generality (you can have a "narrow superintelligence" like a chess engine), and there's how much it knows, which is knowledge base/resource access. But I wouldn't call either of them (super)intelligence.
I notice I fail to see a way to create super-humanly Tall Intelligence that would not quite quickly become very Wide. either the Tall Intelligence would be able to reach sideways, and broaden itself, or it would be trivial to stack a whole bunch of Tall Intelligences working as a Tall Phalanx and thus be functionally Wide.
Wide Artificial Intelligence is simple, hence why we already have it. Making it Wider is easy, just time consuming and lots of legwork. Having a Taller-Than-Human Intelligence would make the process much easier, because (to milk the metaphor dry) A Tall Intelligence can see further, and learn how to reach Wider.