To me, the two ideas are slightly orthogonal. Conceptual skills are cross-domain applicable and is a good measure of your ability to gain new technical skills whereas "technical" in the context I'm using it refers purely to your ability to pierce abstractions in the domain you're working in.

eg: I would be confident stepping in as a technical manager in a software team but if I were to work in eg, aerospace, I'd still have strong conceptual skills but I'd be distinctly non-technical. There's a pretty shallow set of abstraction layers beyond which, I just don't have the education. If I were to go back to school for aerospace engineering, I'm sure my strong conceptual foundation would mean I could master the material 4x faster than anyone else but it would still be a lot of grinding work doing the math and using the software and building prototypes and testing so I could learn. And like, at this stage in my life, the ROI simply cannot pencil out, which is why it's so important to build the foundation when you're young.

I'd say almost every strong non-technical manager is strong on the basis of their strong conceptual skills but that still makes them a non-technical manager and there is a distinct difference.