The second most common type is inflammatory arthritis. This includes rheumatoid arthritis and lupus. These are different. Osteoarthritis is just a mechanical wearing, whereas inflammatory arthritis is actually disease that eats up the joint. It's very important to get a diagnosis early because inflammatory arthritis needs to be treated medically to stop its rapid progression.
Finally, traumatic arthritis is where a person has trauma to the joint, such as a fracture. It heals, but the joint may not heal perfectly smooth, so it will wear out with use over time.