Stream Classic is a standalone app that is not connected with the Microsoft 365 experience. Stream (on SharePoint) seamlessly integrates with apps across Microsoft 365, so you get the same experience no matter where you add or engage with video content. 

For an overview of how Stream Classic and Stream (on SharePoint) differ, please review this article from Microsoft: https://learn.microsoft.com/en-us/stream/streamnew/new-stream/.