I've been a "Principal Engineer" at a large software company and I feel like I embodied each of those archetypes at various points. At various points I was neck deep in critical code, doing the dog and pony show at the executive level, coordinating with other engineering teams and several product managers, and generally doing all of things required to keep pushing something forward.

My relationship with my manager was much more of a peer partnership than manager/IC. I let my manager know what I was up to, progress on things, and any challenges that needed help. The latter bucket was usually empty, but occasionally some cross-org priorities need to be clarified and sorted out.

As others have noted, it really varies between companies, but the main difference between Senior/Staff and Principal is that the latter can be a much more "people" oriented role. You still own and carry the technical vision, but you increasingly interact with non-technical people to enable it and to make it happen.