Docker on Windows appears to be what's coming built into Windows Server 2016? and supports running Windows inside a Docker container and using Windows as a Docker container host. Does this support Linux? I don't think so, I think it only supports running Windows Docker containers. This also appears to be maintained by Microsoft.
Docker for Windows appears to be a separate install created by the Docker team to bring Linux Docker to Windows. So Windows can be the Docker host but all containers are still just normal Linux containers. Does this support Windows containers? I don't think so, I think it only supports running Linux Docker containers. This also appears to be maintained by Docker.
One other interesting note is that Docker Tools for Visual Studio appears to only support Docker Desktop for Windows and not Docker on Windows.
What I'm really looking for are the stated differences bettwen the two, some sort of good comparison. What features are each trying to acheive, where are they similar, where are they different. Will they always be different or will they ever come together?