They can be categorised by how the two bones are joined together:
Gomphoses are found in the sockets of the teeth. The socket of a tooth is often referred to as a gomphosis (type of a joint in which a conical peg fits into a socket). Normally, there should be an absolutely minimal amount of movement of the teeth in the mandible or maxilla.
Synostoses are where two bones that are initially separated eventually fuse together, essentially becoming one bone. In humans the plates of the cranium fuse together as a child approaches adulthood. Children whose cranial plates fuse too early may suffer deformities and brain damage as the skull does not expand properly to accommodate the growing brain, a condition known as craniostenosis.