Top setting (Allium cepa (proliferum group)) and multiplier/ potato onions are unique (Allium cepa Aggregatum group). The other category is somewhat ambiguous, sometimes called bunching onions, shallops, salad onions etc. They may be Allium cepa( the common onion), Allium fistulosum, Allium cepa Aggregatum group. Their common trait is that thier use is as small non bulbing green onions.

The topsetting/Walkin/Tree/Egyptian onion is a perennial onion whose main characteristic is that it sets little onion bulb where the seedhead would form on the other types.
Allium cepa Aggregatum group do seed but are noted for dividing into multiple small bulbs, which are then replanted in the subsequent year. The larger bulbing types are commonly called potato onions altho the term shallot is often applied to the whole group..
Allium fistulosum often known as Welse onions also divide into clusters of little bulbs. Some of them are also perennial. Used as bunching onions

Topsetting onions are extremely pungent, the others will compete with a common storage onion. Sweetest would be the shallot. But a cured potato onion is pretty pungent.

If you really want sweet onions, stick to the sweet varieties of the common onion. Candy, Granex types, Bermudas etc.

Here is a link that might be useful: Egyptian Onion

Farmerdilla, thanks. Very informative description.

I have seen walking/Egyptian onions but never planted/had one. I got to get some somehow. It is very ornamntal , to me.