It's all about where the packages and services are installed
No. Your packages and services could be on a network share on the other side of the world, but where they are run is what matters here. Processes are always loaded into, and run from main memory.
"Running on bare metal" refers to whether the CPU the process is being run on is emulated/virtualized (ex. via Intel VT-x) or not.
A VM uses virtualization to run an OS, and the processes are running within that OS, thus neither is running on bare metal. But the purpose of containers is to run them wherever your host OS is running. So if your host is on bare metal, then the container is too. You are not emulating or virtualizing any hardware.