That is the case I think, the two ideas about types of professional networks seems clear, and it would seem I probably see it differently to some. To me, "professional network" is better at describing a network curated for your career.

It's a tough one, because while I can see that it is also a professional network, said network would be pretty offended if I called them that. So I don't necessarily disagree with you, or even with the other commenters, but there is at least some room for subjectivity about what to call your own personal relationships.