How does gout/pseudogout relate to arthritis?

Both are arthritis. Gout and pseudogout are both types of inflammatory arthritis. Gout is caused by uric acid crystals in the joints. Pseudogout is caused by calcium pyrophosphate crystals. Both gout and pseudogout can cause attacks of arthritis causing pain and swelling in joints. The symptoms can be similar. It is important to get the right diagnosis, since the treatment for gout and pseudogout are different.
Gouty arthritis. Repeated attacks of gout can cause joint cartilage destruction which is a form of arthritis. The repeated inflammation of the joint can cause dissolution of the cartilage.