The main difference is the commercial aspect (as in “revenue stream for Docker”), as pointed out in this Techcrunch article from Frederic Lardinois (@fredericl):
The idea behind the store is to create a self-service portal for Docker’s ecosystem partners to publish and distribute their software through Docker images — and for users to make it easier to deploy these applications.
While Docker already offered its own registry for containers (DockerHub: https://hub.docker.com/explore/), too, the Docker Store is specifically geared toward the needs of enterprises.
The store will offer enterprises “with compliant, commercially supported software from trusted and verified publishers, that is packaged as Docker images,” the company says, and feature both free and paid software.
Unsurprisingly, Docker will take a cut when a user installs a paid application through the store (though what exactly this revenue share agreement for paid-via-Docker content looks like is currently unclear).