Thanks for the post! As BGanger mentioned above, the tutorial site is not directly affiliated with TestRail, and may not have the most up-to-date information or screenshots, so bear that in mind.
That being said, in a brand new instance or trial of TestRail you’ll see the bar at the bottom as a sort of guide that will take you through setting up the basic entities to help a new user get started. Once all of those steps have been completed it can be dismissed, and will not appear again. The section above that displays the projects will display the large icon and project name for any currently active projects, but if a project is marked as completed you’ll see the small icons as in your view. It also appears the project names may have been removed, which would explain why you’re only seeing the small icon and project details.
I hope that clears things up!