I can't see the first image, but some things to check would be if there are any sorts and filters applied to either of the views (users can apply their own sorts/filters on top of views). That will make the project look different even if both users are on the exact same view.
View Differences for Same Project
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Cant see the first image, but each user is allowed to set their own filters and views of each project. They also have the options to save as their default. Make sure your Project view is the same
An Clarizen Admin may have the option to set permission on the different type of views a User can see.