The most common and recognizable goldfish variety is the standard comet goldfish. These long body goldfish come in a variety of white, brown, gold, and red colorations and grow very large very quickly.
Very similar to the comet goldfish is the Shubunkin goldfish. They have the same long body as a comet, but their fins are longer and display a calico coloration with a mix of black, red, white, and blue pigments.
Also known as "painted goldfish," Sarasa goldfish closely resemble the kohaku koi with vibrant red and white patterns. The Sarasa goldfish has a long body and fins, making them an appropriate species for both indoor and outdoor aquatic systems.
Starting with the fancy goldfish varieties is the fantail goldfish. This variety has been bred to have a double tail, fused along the dorsal edge. The fantail has a medium to short body profile, giving it some swimming difficulties.
Oranda Goldfish have a double tail like the fantail goldfish, but also they are known for their wen on top of their heads. This is a benign growth of the skin tissue that can overgrow with improper diet and wonky genetics. An overgrown wen requires trimming by your veterinarian.
Ryukin goldfish are distinguished by their very short body and protruding hump behind their heads. This variety comes in red, black, white, or a combination of colors, but they are very poor swimmers, so your aquarium can be smaller in order to accommodate their lack of vigorous motion.
Ranchu goldfish have round, hunched bodies and lack a dorsal fin. Their tail peduncle points downward, making it difficult to swim for long periods, so smaller tanks are appropriate for these fish. Your Ranchu may or may not have a partial wen on his head, cheeks or operculum (gill cover).
Very similar to a golf ball with fins, the pearlscale goldfish has a severely shortened, rounded body with raised scales that have the appearance of tiny pearls. They may have a remnant of a wen on their head and come in a wide variety of colors.
The black or red Moor goldfish, also known as the telescope eye goldfish, are known for their short bodies and protruding eyeballs. Given their presentation, these fish do not see very well, so they take a little bit longer to eat and are prone to cuts and tears on their delicate eye conjunctiva.