This style of omelet is often called a French omelet, but it is not a French omelet. It was probably devised by cooks who hesitated to tackle the French method.
It is made somewhat like a French omelet, except low heat is used and the eggs are not stirred or agitated. Instead, the edges of the cooked portion are lifted with a fork or spatula, allowing the uncooked portion to flow underneath. The finished omelet may be folded in half or like a French omelet.
The advantage of this method is that it is easier to learn.