That's it. That's the entire thing. Plus some nuance about things that self-replicate faster than other things...
It occurs at all levels. Amyloid protein in Alzheimer's patients is self-replicating. So are cells. So are individual parts of cells. Sometimes things replicate by being parts of a larger thing that replicates, sometimes they don't. It's all one big chaotic tangled mess with no particular purpose or design. Human cells evolve, so do humans, so do human societies. So do rocks.
And amyloid protein doesn't self-replicate. An instance of the misfolded form causes other folded proteins of the same type to transition to the misfolded form. It's a form of catalysis, not self-replication.