In the U. S, the Mini Lop is not a dwarf. The dwarf in the family is the Holland Lop (adult weight 3-4 lbs; the dwarfing gene is required to get the correct proportions).
Holland Lop
The Holland Lop spawned a long haired twin, called the American Fuzzy Lop. They pose differently, but size-wise are pretty much the same.
American Fuzzy Lop
The Mini Lop is an older breed, and a bit larger, weighing about 6 lbs.
Mini Lop
There is frequently a bit of confusion about the names of the smaller lop breeds. In other English speaking countries, what we call a Mini Lop is called a Dwarf Lop, but even there, it isn't a dwarf breed (involving the dwarfing gene). They call the dwarf breed (our Holland Lop) the Mini (or Miniature) Lop. Confused yet?
OK, how about the fact that with an awful lot of people, any rabbit that has ears that don't go up gets labeled a Mini Lop (kinda like how any large breed dog that doesn't have a short, slick coat "looks like a German Shepherd")? If I've heard it once, I've heard it a hundred times: "we got a Mini Lop when I was a kid; it grew up to weigh, like, 12 pounds."
The Mini Lop got its name from the fact that it was bred as a sort of scaled-down version of the French Lop; which at 11 lbs+ is a bit more rabbit than most people are looking for as a pet:
French Lop
I suppose, since I seem to be writing a treatise on Lop breeds, I should go ahead and finish out the class . . . .
Not all lop breeds have wide muzzles; the English Lop has a relatively narrow one, but it also has amazingly long ears. In fact, ears that are too short is a DQ on a show table. It's also a large breed, weighing 10 lbs or more:
A new breed that is rapidly gaining popularity is the Velveteen Lop. Type-wise, it's a scaled-down version of the English Lop, and is unique in having Rex-type fur:
Did I miss anything?