The Docker Platform is the industry-leading container platform for continuous, high-velocity innovation, enabling organizations to seamlessly build and share any application — from legacy to what comes next — and securely run them anywhere
LXD isn't a rewrite of LXC, in fact it's building on top of LXC to provide a new, better user experience. Under the hood, LXD uses LXC through liblxc and its Go binding to create and manage the containers. It's basically an alternative to LXC's tools and distribution template system with the added features that come from being controllable over the network.
KVM (for Kernel-based Virtual Machine) is a full virtualization solution for Linux on x86 hardware containing virtualization extensions (Intel VT or AMD-V).
Virtuozzo leverages OpenVZ as its core of a virtualization solution offered by Virtuozzo company. Virtuozzo is optimized for hosters and offers hypervisor (VMs in addition to containers), distributed cloud storage, dedicated support, management tools, and easy installation.
Kubernetes is an open source orchestration system for Docker containers. It handles scheduling onto nodes in a compute cluster and actively manages workloads to ensure that their state matches the users declared intentions.