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.
> the differentiating feature between lxd and podman seems to be that lxd can manage full virtual machines
LXD is a management layer over LXC and Qemu(KVM?). LXC is all about system containers. The Qemu support is a recent addition [1]. LXD supported only LXC system containers until then.
> Containers you run with docker and podman are fully capable of running multiple processes
Yes. I have done this. But it was very unwieldy - probably because docker, podman etc weren't designed to run system containers.
K8s doesn't support orchestrating LXC/LXD containers as far as I know. What I did was to use LXD containers as hosts/nodes for K8s. So, it was basically application containers/pods and K8s running inside system containers.
In addition, there are orchestrators which can run LXC containers (LXD is a management layer over LXC). Hashicorp Nomad is noteworthy.
Added later: K8s runs OCI containers. All OCI containers I have seen are application containers. I don't know if OCI specification supports system containers.
I have used both lxd and podman.