View settings are essentially global. You can't simultaneously show different layer setups in different viewpoints.
You're in plan, looking at a plan view with plan layers (the layers saved with that view). Double-click a Section view in the view map, you get the section, showing the layers saved with that view. If you switch back to the plan by clicking in its window, you will see the plan window with the section's layers. I'm sure multiple simultaneous views is a wish.
The difference between the Project Map and the View Map: When you open a view, that viewpoint opens and all the view's settings are activated. When you open a viewpoint from the Project Map, you get that viewpoint with the current settings.