Power Bi Apps

The type of app you are referring to is known as a "Workspace App".  It can only include report items from the same workspace (i.e Power BI Report, Paginated Report, Dashboard).  What is important to understand is that you can take a report, remove its underlying semantic model and then make a live connection to another model inside the Power BI service.  This can allow you to publish a clone of a report, without having to clone the model.  You can host that clone in your workspace where you wish to include the app.
Workspace apps in Power BI - Power BI | Microsoft Learn

Separate reports from models in Power BI Desktop - Power BI | Microsoft Learn

Org apps are a new evolution of the workspace app.  They still can only use objects inside the single workspace but have the ability to host more Fabric items than just the reporting elements.
Get Started with Org Apps - Power BI | Microsoft Learn

Hello mp390988​,
A useful distinction is that Org Apps are not a Premium-only feature. They can also be used in Pro workspaces, subject to the applicable licensing and permissions.

Both Workspace Apps and Org Apps have a single-workspace content boundary, so neither allows you to directly combine items from multiple workspaces.

The key difference is that Org Apps extend content distribution beyond traditional Power BI reporting to support additional Fabric items and multiple apps within a workspace.

There is no need to abandon your existing Workspace Apps. They remain a valid option for distributing Power BI reports and dashboards. Consider Org Apps when you need their extended Fabric capabilities.

Documentation:

• Get Started with Org Apps

• Workspace Apps in Power BI