I haven't read much about lxd until just now but based on that link, the differentiating feature between lxd and podman seems to be that lxd can manage full virtual machines (using qemu as backend, according to [1] which was linked elsewhere in this thread). Whatever this distinction is between application and system container, it doesn't appear to be a technical distinction nor a feature that lxd has that podman lacks, unless I'm wildly misunderstanding it. Containers you run with docker and podman are fully capable of running multiple processes (in my experience it's quite common to do so) and Red Hat has blog posts from years ago specifically discussing running systemd in podman, eg [2]. Managing VMs is indeed an additional feature though.

[1] https://ubuntu.com/blog/lxd-virtual-machines-an-overview

[2] https://developers.redhat.com/blog/2019/04/24/how-to-run-sys...