I am very unclear when to use which. If I want to make restrictions so that each department sees something different, which is best to use?
here is a link that may help https://knowledge.domo.com/Connect/Personalized_Data_Permissions_(PDP)/PDP_vs._Publication_Groups
Sounds like you want Pub Groups if you want to control what they see. But if they need to communicate with another dept...then that would cancel that and you'd go PDP.
In the past I've created pages with cards w/ filters...then giving access to those pages/cards to just Domo Groups...so that users can communicate/share with each other regardless of dept. Not sure if that is best route...but it works.