Basically the leather is categorized into 3 : Genuine leather, top grain, and full grain.
Full grain is the most expensive one (and supposedly the most desirable) because it requires the least synthetic materials. The reason is that full grain is the closest to the outer skin of the animal. The deeper it goes, the less dense the texture is and the more synthetic materials needed to make a glitter leather.
The deepest level of layer is genuine leather, which also connects to the flesh of the animal. This is the cheapest one because it has the least dense texture, which requires the most synthetic materials to make a real leather.
Top grain is in the middle between those two.
So the order goes like this (from most expensive/closest to outter surface) :
1. Full grain
2. Top grain
3. Genuine leather
Genuine leather on a tag is most often used to describe the cheapest form of leather, which, as stated already is split leather and coated to give either a smooth or textured finish
Genuine Leather means 100% pure leather which is made of the animal skin itself. Not the mixture or any other layer above it. After removing the unwanted hair, it is made with the skin by drying and tanning it up.