Consider yourself corrected then. A portable system has it's own display method included and built-in to the unit, but it's also not a handheld because you don't play it, solely, in your hands. You have to rest it on some sort of surface whether it be a table or even your lap. Comparing game systems to computers - it breaks down like this;
Desktop Computer = Console
Laptop Computer = Portable
Palm Computer = Handheld
Seriously though, calling the distinctions "portable consoles" and "home consoles" is exactly the same thing. Just different terms.