Okay, first a teminology correction...it's not double die...it's doubled die...with a D on the end of the first word. This term means a doubled design on a die, not two strikes or two dies - so it's not seeing double...it's doubled.
Second...a doubled die is the result of the hubbing mechanism imparting its design onto a die out of alignment with any one (or more) previous hubbings. In the past dies required more than one hubbing to completely sink the design into the die, and various methods were used to ensure the die was aligned in the press identically every time it needed to be hubbed. Sometimes these methods failed, thus allowing the design to have a doubled appearance on the finished die.
The reason why doubled dies do NOT have to encompass the majority of the design is mainly due to the fact that dies start out with a conical shape to help the metal flow properly toward the outside of the design during the hubbing process, and to require somewhat less pressure to impart the entire design onto the die. Because the dies started out with a conical shape, the center of the deisgn would be hubbed first, then a little more and a little more outward with each subsequent hubbing. If the first hubbing was out of alignment with the rest of the hubbings, the only part of the design affected would be the center.
With the newer dies (1997 to present) the dies were created with one single pressing of the hub, thus removing the possibility of most styles of doubling. The one typical exception is the moment after the hub begins to press downward on the conical shaped die. If the die is out of alignment slightly, the pressure causes it to snap into alignment when the pressure begins, but by this point the center of the design has already been pressed into the die. The amount of pressure and design features pressed into the die at that point determine whether there will be any doubling and how strong the doubling is.
The main difference between hub doubling (doubled dies) and "machie doubling" is that in hub doubling the doubling is on the die before the die is used to mint coins. It is imparted to the die at the time the die is made.
Machine Doubling is the result of a loose die on a coining press. The die bounces on the coin partially flattening the design in some areas. While these two types of doubling are somewhat similar, they are very different in creation. Hub doubling, or doubled dies, are actually quite scarce, while
Machine Doubling is very common and is not considered collectible for value.