Yes that's correct. It's the .aprx file. (And Yes it's very confusing especially for those users who haven't used a ribbon environment such as new versions of AutoCAD.) However, you cannot just create a "document" as you do in ArcMap. It's very different from the ArcMap approach. ArcPro has a completely new interface that is Project- based rather that a single document-centric. By default, when you create a new project, a project geodatabase, project toolbox, default folder is also automatically created within the project structure hierarchy. You can then insert multiple maps, scenes as well as multiple layouts and insert various maps on any layouts. It's actually more similar to AutoCAD then ArcMap - in autocad you work on a model space and you can then create multiple layouts with viewports into the model space.
Also by default, when you insert a new map to your project it's set to the ESRI topo basemap. You can customize some of this behaviour in the Project Options: Project Tab -> Options -> Map and Scene -> Basemap.
However, I am not sure why, you currently cannot customize the behaviour for creating Project Files: Pro will create the default project items. You can only specify in which location or what database. Hopefully a 3rd "none" option will bee added in future release so that users are not forced to create the project structure.
As a side note, you will have to completely rethink how you use tools and properties in Pro: Just like in AutoCAD, the ribbon-based approach is CONTENT SENSITIVE. In other words, when you click on an item in say the TOC only those tools and commands pertaining to the operations for that particular item will be active on the ribbon.