Strictly in regards to long single tailed variety of goldfish, I believe a comet can be all gold, yellow, or have any amount of white including all white. If it has blue or black it becomes a shubunkin. Until there is a similar organization to fish as there is a.k.c. to dog breeds I believe there is no single easy answer to the question.
Taken from:
http://www.fishpondinfo.com/fish/gfbreed.htm
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Common - single tail; no adornments; usually natural bronze or reddish orange with white on the fin tips but may be other colors;
picture
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Comet - single long tail; no adornments; essentially long finned common goldfish; usually orange with or without white or black on fins; often change colors as age
Shubunkin (original) - single short tail; no adornments; mix of white, red/orange, and blue/black
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Bristol Shubunkin - single long tail; no adornments; mix of white, red/orange, and blue/black
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London Shubunkin - single short tail; no adornments; mix of white, red/orange, and blue/black; known for its intense blue
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Fantail - double tail; fat bodied; red, white, calico, or any combination
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Veiltail - double long tail; fat bodied; red, white, calico, or any combination
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Lionhead or Ranchu - short double tail; no dorsal fin; fat bodied; hood or growth on head; red, white, calico, or any combination
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Oranda - long double tail; lionhead with dorsal fin; less fat bodied; hood or growth on head; red, white, orange-yellow, red cap (red just on hood), calico, black, blue (gray), chocolate (bronze), brown, or any combination;
picture blue oranda;
picturecalico oranda with torn fins;
picture red cap oranda
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Telescope eyed - double long tail; with or without dorsal fin; fat bodied; large eyes; developed from veiltail; red, white, calico, or any combination
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Black Moor - double tail; deep black color; large eyes; essentially a black telescope-eyed goldfish
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Bubble-eye - double tail; fat bodied; no dorsal fin; large fragile sacks around eyes filled with fluid; developed from celestial; red, white, calico, or any combination
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Pearl scale - double short tail; fat bodied; protruding scales as if fish has dropsy; red, white, yellow, calico, black, chocolate, or any combination
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Pompoms - double tail; fat bodied; no dorsal fin to be "prized" fish; may have other adornments; pompom like growths near nostrils; red, white, calico, or any combination
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Celestial - double tail; no dorsal fin; upturned fragile large eyes as adult; red, silver, orange-yellow, white, or any combination (usually metallic)
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Wakin - double short tail; bright colored; yellow, orange, white, or red-orange and white
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Peacocktail - tail like a butterfly; developed from Wakin; red, white, calico, or any combination
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Fringe tail - double large tail; fat bodied; hump on back; red, white, or any combination
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Albino doll - double tail; fat bodied; large eyes; albino telescope eyed-like fish