Lightning HOME PAGE Design / Assignment

In Classic, it appears that the configuration and assignment of our Home pages were based on user profile.  So, for example, those individuals labelled 'superusers' received the same Classic HOME page even though each 'superuser' may belong to a different functional group.

With Lightning, we are looking to design and assign HOME pages based on their functional group so that all members of a functional group will have access to the same HOME page features.

We are struggling a bit trying to determine how best to make this transition.  I'm thinking that the answer may involve defining different Apps and assign the new Lightning HOME pages to a combination App and Profile.  (What's confusing a bit is trying to understand what the definition of an App is within the App Launcher - we see apps in the App Launcher that are not truly independent apps but appear to be related to a single app - just configured for a different role and the only difference is the tabs on the Navigation Bar) 

Any suggestions would most certainly be welcome on how best to try and approach this.

Thank you