Hello JSW W.,
I will try to answer you to the questions that you ask above.
"So how do you know which one to use for?"
Basically this depends on your decision and the functionality of the application that use them. Good example is the Visual Studio IDE.
"Can DockingPanel be rename by double click?"
This functionality was recently added to the NUIDocuments when they are in MdiTabbed view style. However it doesn't apply to NDockingPanel because double clicking on the panel header has different meaning, namely switch the panel state from docked to floated and opposite.