Is it possible to select items in the 3D Window and keeping the selection in plan? And why can we select different items in 3D and in 2D?
Yes, it is possible and to do this, the best method is to use the Selections Palette.
Step 1: Select items in the 3D Window
Select the items in the 3D window that you would want to be selected on the Floor Plan as well.
Step 2: Open Selections Palette
Activate Selections Palette from Window menu/ Palettes/ Selections
Step 3: Add Selections
From the pop-up menu (click on the arrow button at the top of the palette) choose "Add selection..." command to save the selected elements to your list. (click on the arrow to the top right for the pop-up menu)
Step 4: Go to the Floor Plan
Use the Selections Palette to select the saved selection again: select the saved selection, then click on the '+' sign
Why can a selection in 2D be different from a selection in 3D?
Eric Link's answer is accurate as can be:
It is 'by design' that we can have something selected on the floor plan (or even section/elevation) and something completely different selected in the 3D window. It enables us to further refine what we want to see. For example if we select 10 things in the floor plan and choose to 'Show Selection/Marquee in 3D', then once in 3D we can choose just 5 of those elements and do it again, to show just those 5 elements in 3D. Then we can toggle between those and showing All (not the original 10, but everything), and then reselect other things to show in 3D - all within the 3D window!