The "New Reports" folder is where all your new reports end up as they are received.
The "All" selection will show you the reports in all your folders together.
Although the name might be confusing, new reports refers to reports you have not specifically sorted into another folder, and they include opened reports as well (that don't show (new) in the title).
Furthermore, those reports you saw in the "All" category with (new) in the title were Loot Assistant reports. You will find them again when you open "Loot Assistant". Unlike all other reports, Loot Assistant reports are automatically placed into the "Loot Assistant" folder by the system.