Elastic scattering can be categorized into two main types: Rutherford scattering and Bragg scattering. Rutherford scattering occurs when charged particles, such as electrons, are deflected by the Coulomb forces of the target's nucleus. Bragg scattering, on the other hand, involves the diffraction of waves (like X-rays) by a periodic array of atoms, leading to constructive and destructive interference patterns.