With the Photon open source project, VMware hopes to build a community around the practice of running containerized applications in virtual environments. Photon is an umbrella term for multiple projects that include ways to deploy containers on a VM, using Photon OS, as well as ways to deploy containers as VMs on VMware infrastructure.
Photon OS is a small-footprint Linux container host designed to run on virtual machines and tuned for VMware hypervisors. VMware has certainly embraced the Docker movement in a big way, and not just on VMware. You can run Photon OS on other hypervisors including Google Compute Engine and Amazon EC2. However, you cannot install Photon OS on a physical server.
Photon OS does not make assumptions about the container toolset, although Docker is installed by default. Administrators can layer container management tools of their choice over the base OS using the Photon package manager.