Storage drivers help manage storage on images and containers.
Volume drivers help manage persist storage.
Volumes are handled by volume driver plugins the default volume driver plugin is local. The local volume plugin helps create a volume on the Docker host and store its data under the Docker volumes directory. There are many other volume driver plugins that allow you to create a volume on third-party solutions like Azure File Storage, gce-docker, Net App etc.
When you run a docker container, you can choose to use a specific volume driver such as the rexray/ebs to provision of volume from Amazon ebs