Question

what is the defining difference between a handheld or mobile console and \home\ consoles like the atari, nes, or playstation 4?
the size of the console
whether they require a television
the complexity of controls
the type of games they offer

Explanation:

Handheld consoles have built - in screens, so they don't need a TV. Home consoles like Atari, NES, or PlayStation 4 rely on a television for display. Size, control complexity, and game types can vary within both categories and aren't the defining differences.

Answer:

whether they require a television