May you write me what is the difference between the fusion and latent melting heats in the case of sapphire, please? What their physical meanings are?

The fusion heat is heat necessary for begining of melting. Latent melting heat is heat which we have to add all time until all material will be in view of melt. The temperature of material is constant in this period of time. The simple example: ice bit in any water. Water is cooling, but temperature of ice is constant all time until ice “is living”. Sapphire, ice — not difference.