The whole thing with LXD’s command line tool being named lxc was an attempt by Canonical management to get some free press for LXD and try to get people to transition from traditional LXC to LXD. That went as far as attempting to rename the existing lxc package to lxc2 with LXD then being lxc3.
That never really took off and things have generally reverted back to the old state now with the lxc package being the actual LXC project and LXD being its own thing distributed as a snap.
But LXD keeps on using the lxc name for its command line tool, causing a lot of confusion…