LXC and LXD are two different things. When you apt-get install lxc you get the C tools to manage liblxc, those come as lxc-XYZ binaries and use configuration as text files in /etc/lxc/ and the like.
LXD is a different beast, it’s a daemon with a database, it doesn’t store any config in /etc and has a single command line tool (confusingly) named just lxc.
The pinned topic at the top of this forum may help too: Comparing LXD vs. LXC