LXC
LinuX Containers (LXC) is an operating system-level virtualization method for running multiple isolated Linux systems (containers) on a single control host (LXC host)
LXC is a command line tool that calls REST API locally or remotely.
LXD
by Canonical, Ltd
a container system making use of LXC containers
so that you can: run LXD on Ubuntu and spin up instances of RHEL, CentOS, SUSE, Debian, Ubuntu and just about any other Linux too, instantly.
LXD is a daemon service that exposes REST API and manages the containers via liblxc.