A PaaS host saying they supported Docker would imply that they'd be using, for example, SquashFS for container format, AuFS instead of OverlayFS for union-mounts, LXC instead of OpenVZ/Xen/KVM for isolation, and any other set of things your container might subtly rely upon.
The culmination of this, I imagine, would be a PaaS host allowing you to specify the "stuff" you want to run just by the URL of the container-image.