The fact that there are so many base images including an init system and even Docker now includes a small init that you can activate with a command line switch might give an indication that many people are using Docker for "system containers".
if you’re looking at the kernel features used (namespaces, cgroups, etc) containers are multiprocess (even with docker you can go attach into the container and look at things).
This may be semantics, but the first process in the container is an “init” regardless if it’s a proper init or just a process.
As far as light-weight VMs: containers are supposed to be lightweight VMs (But defining lightweight can be challenging)
let's agree to disagree on this one. I am not sure that system and application container are or should be different, but it's okay if we have a different opinion.