What small difference is there between the black horn and white of hooves?

There isn't really a "white" part of a hoof. The term "white" is often used to describe the hoof wall, the hard outer layer of the hoof.

The black horn is the sole of the hoof, the soft, fleshy part that sits beneath the hoof wall and provides cushioning.

So, the main difference is location and texture.

* Black horn (sole): Soft, fleshy, located on the underside of the hoof.

* White (hoof wall): Hard, tough, outer layer that protects the sole.

It's important to remember that the color of the hoof wall can vary, and "white" is just a common term. Some hooves are actually brown, grey, or even black.