Why is Vagrant not considered an isolation, and Docker is, when Vagrant run a new OS and isolates everything in there? What is meant by isolation when one says: “if you’re looking for isolation, use Docker”?
Isolation in the meaning “only isolation” i.e., not virtualization. When you want to run linux apps on linux, we are talking about isolation; when you want to run any app on top of any os, then we talk about virtualization.
Where did you read that Vagrant was not considered an isolation?
Actually, this statement is true as Vagrant is not a Container backend nor a VirtualMachine. It is a manager. It can manage VirtualBox, VMWare and now Docker. Depending on what your needs are, you can achieve isolation through Vagrant via VirtualBox or Docker, but Vagrant does not provide the isolation by itself.
Now that Vagrant supports Docker, you can use it if you need to; however, Docker is very simple by itself and IMHO does not require a tools like Vagrant. When you are playing with Virtual machines, on the other hand, Vagrant is very helpful.