Actually you're still a bit off. This is in reference to libcontainer vs lxc only.

libcontainer is a native golang library for accessing all of the linux namespace and cgroup features of the linux kernel.

lxc is a project that bundles the namespace and cgroup isolation features of the linux kernel into a simple set of command line utilities.

Both are not "implementations of an idea". They are abstractions ontop of the kernel features.

Edit:

For the parent, s/Libvert/libvirt/. It is a virtualization abstraction library written by Dan Berrange and the Redhat crew.