I think Docker can somewhat be seen as a generalized term like Linux. Linux doesn't write EXT4 but it is often referred to as "Linux filesystem".
Docker has been actively trying to become to household brand name for containers so it's difficult for me to give them a pass with your line of reasoning.
> Re Persistent Data: You are probably going to have a tough time if you try to do persistent data. Containers really excel at stateless tasks(or temporary state like caching). Certainly it's doable but for someone early in their adoption the proper toe in the water is probably the stateless business logic not the state layer.