AFAIK Docker, LXC, Podman, etc. are actually all the same underneath: they use 'runc', which chroots into a directory (along with extra restriction/config via cgroups, bind mounts, etc.).
The differences between Docker, LXC, Podman, etc. are the config, management, etc. of containers; e.g. Docker abstracts over the chroot directories, using a set of content-addressed tarballs (called "images"), and provides commands for starting/stopping/listing/etc. the containers that are running.
Dating myself a little, but LXC came along well before runc. It predates Docker, and was actually wrapped by the first versions of Docker. I learned about LXC, and used it, after doing some research on how to build my own PaaS at work (pre-Docker) and reading that Heroku was using LXC for their platform. It worked decently for me, but required more in-depth knowledge of all the knobs for disk mounts and networking than Docker typically requires.
You may be right that LXC has switched over to runc since then. I haven't kept up. I would be surprised though.
The differences between Docker, LXC, Podman, etc. are the config, management, etc. of containers; e.g. Docker abstracts over the chroot directories, using a set of content-addressed tarballs (called "images"), and provides commands for starting/stopping/listing/etc. the containers that are running.