The distinguishing layer between hexagonal close packing (HCP) and cubic close packing (CCP) is the third layer. This can be explained as follows:

1. Basic structure:
Both HCP and CCP are types of close packing structures, where the spheres or atoms are arranged in a closely packed pattern. In HCP, the spheres are arranged in a hexagonal pattern, while in CCP, they are arranged in a cubic pattern.

2. Layers:
The packing pattern in both structures can be described in terms of layers. In HCP, the first layer consists of spheres arranged in a hexagonal pattern, and the second layer is also hexagonal, but shifted by half a unit cell. The third layer is again identical to the first layer, and so on. In CCP, the first layer consists of spheres arranged in a square pattern, and the second layer is also square, but shifted by half a unit cell in both directions. The third layer is again square, but shifted by a quarter of a unit cell in both directions, and so on.

3. Distinguishing layer:
The third layer in HCP is identical to the first layer, which means that the spheres in the third layer occupy the same positions as those in the first layer. In other words, the third layer completes the first layer to form a three-dimensional hexagonal pattern. On the other hand, the third layer in CCP is not identical to the first layer, but is shifted by a quarter of a unit cell in both directions. This gives rise to a cubic pattern in three dimensions.

Thus, the distinguishing layer between HCP and CCP is the third layer, which completes the hexagonal pattern in HCP and gives rise to the cubic pattern in CCP.