"Sets" are what you plant if you want scallions. Transplants are what you plant if you want onions later. Don't know about the varieties of sets. I always buy transplants with given names to know what I will harvest. Last (and this) year I am doing 'Texas Sweet' and 'Candy'. Yummo.
hortster

Survivalist, you're right. Sets are tiny little onions, about marble sized. Transplants are little onion plants. Both will grow and produce onions the year they are planted. Sets and transplants can be labeled varieties or just called "onions" depending on who you buy them from.
I don't like sets very much and prefer to grow my own transplants. Sets tend to flower rather than bulb, at least for me.
-Mark

Sets that have been held in cold storage are easily triggered into bolting, as they are no longer juveniles. Seedling plants are juveniles, and must be abused pretty bad to be triggered into bolting. The big diff is life stage.

Onions generally do not flower till the second year.
Sets are one year old plants, which is why they flower.

Transplants are just that young plants less than a year old to be transplanted.

Depending on where you get your sets depends on whether or not the type is identified.
Many "catalog" places now identify their sets.