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Docker is not a "jails" clone. (Linux has had "jail" like containers, called LXC, for almost 10 years now.)

Docker runs on top of lxc if I am not mistaken.

It used to run on top of lxc but it was replaced by https://github.com/opencontainers/runc if I'm not mistaken.

Not anymore - it used to. Still uses Linux namespaces and changeroots.