The red-cap oranda is a variety of goldfish. Goldfish have been bred in many distinct varieties with different colors and body shapes.
Observe the tail
If the tail has a single fin, it is not an oranda. Orandas have a double tail. Single-tailed goldfish include the comet, the shubunkin and the common goldfish. Many varieties of goldfish other than the oranda have a double tail.
Study the body shape
Orandas have a squat, egg-shaped body. Double-tailed goldfish that don't have egg-shaped bodies include the sakura, the wakins and the jikins.
Check out the head
Orandas have a growth on the head, called a wen, that looks kind of like a cap or warty covering. Young orandas may not have developed an obvious wen yet. It takes around two years for the wen to fully develop. Some pearlscales have a head growth, but it looks more like a bubble than a cap. The scales of the pearlscale are also very distinct from the oranda's scales. Pearlscales have a hard raised area in the center of each scale.
Investigate the color
Red-cap orandas have a white body and a red-colored wen. The eggfish sometimes has a red head and white body, but it is lacking a wen. Orandas can grow up to 10 inches long. They have long, flowing fins.