It is confusing, I agree. IMO we should have "self-running" and "self-hosting". Self-running if I provide the hardware, self-hosting if I manage it. Or swap the term, still not sure but there is a difference between you are the one maintaining it and where does it run.
I gave it a second thought and I think terms should be "self-managed" - you manage it either locally or in cloud and "self-hosted" you host it locally. Idk "self-contained" doesn't click with me, to be fair.
Whether you use the cloud, or a vps, or a dedicated bare metal server, or your own equipment at home is all self hosting.