In simple terms, a Connect User has full functionality in Vertex. This means that they can import 3D models, create workspaces, add workspace members, merge models and use all the features in the 3D Viewer to interact with the models. This includes taking snapshots, creating stories, and sharing those stories with others who are not already a Connect user.
A Story user has 3D functionality in Vertex's Story Viewer, and can open shared Vertex Stories. They cannot import in the 3D Viewer. However, they have all of the features that they need to collaborate effectively on a story, such as adding comments.
For more information on what both types of users can do in a collaborative story, see What can collaborators do in a story?