Ususally, the terms egyptian and walking onions are used interchangeably. These onions produce small to moderate sized bulbs at the base and small onions (topsets) instead of a flower at the top of the stalk. Multiplying onions only produce a bunch of small to moderate sized onions at the base of each plant and a normal allium looking flower stalk.

I've only used them for pickling so I don't know how tough they'd be if used as regular onions but since they're smaller than regular onions, they might be a little tougher - like I find for some shallots.