Which is:
Containers are not actually a _thing_. BSD Jail is a _thing_, Zones are a _thing_... Linux containers are just a particular configuration of _multiple things_.
PIDs in containers CAN be like PIDs in BSD Jails... if that is what you want. It's up to you to use what Linux primitives you want in your containers.
For example:
I can run a application in a 'linux container' that shares PID, user, and network namespace with the main OS.. and the only thing that is different is that the file system is namespaced. I can run cgroups without running namespaces. I can run namespaces without cgroups.
Now if you want to talk about _Docker containers_ then, yes, that is a _thing_, but it's just one of many different possible ways to have Linux containers.