To “greenthumbnail”:
Common Goldfish - Common goldfish, or Hibuna in Japan, are a type of goldfish with no other modifications from their ancestors other than their color. Most varieties of fancy goldfish were derived from this simple breed. Hibuna come in a variety of colors including red, orange/gold, white, black and yellow or 'lemon' goldfish. The Common goldfish has a single tail, nothing really special. They are extremely streamlined.
Shubunkin (SHOE-boon-kin, meaning “red brocade”)– Sometimes described as “calico” the basic body color must be blue (at least 25%), it must contain red, and it must contain black spots that extend into the fins and tail. It may also posses overlapping patches of orange, gold, white, grey and black (along with dark spots). Blue is the most prized color in shubunkins, the more the better. (A few new varities are being developed that are all blue, inspite of the calico description.) There are three varieties of Shubunkin; Bristol, London and Japanese/American.
Wakin - The Wakin (wa-keen or wah-keen) is a Common goldfish with a divided, fantail-like tail and is the Common goldfish of the Far East, particularly in Japan; in fact, our Western Common goldfish with wild-type, single fins all round is uncommon in the Far East.
Depending whom you ask, there are between 20 and 29 varieties of goldfish (to nit-pick, some claim as many as 300). The most common are:
1. Black or Broadtail Moor – Black Peony, Popeye, Telescope, Demekin Moor, Black Dragon-Eye
2. Bristol Shubunkin – Bristol Blue Shubunkin
3. Bubble Eye – Froghead, Toadhead
4. Celestial – Choten Gan, Demeranchu
5. Comet – Comet-Tailed Goldfish, Kometto, Swallowtails
6. Common – Hibuna, Gold Carp
Crown Pearlscale - Hama Nishiki
7. Eggfish – Maruko
8. Fantail – Western Ryukin
Fringetail – (considered by many as the long-tailed version of the Ryukin)
Shubunkin – Japanese/American Shubunkin, Speckled Goldfish, Harlequin Goldfish, Calico Goldfish, Coronation Fish (considered by many as a calico colored Comet)
9. Jikin – Butterfly Tail, Star Tailed, Peacock-Tail
Lionchu – Lionhead-Ranchu (a cross between the Lionhead and the Ranchu)
10. Lionhead –
London Shubunkin – Londonderry (considered by many as a calico colored Common)
Man-yu – Oriental Twintail (the common Chinese Twintail, an intermediate between the Fantail and ……. .the Veiltail)
Nankin – Izumo Nankin; a tranditional white and red Ranchu variant
11. Oranda – Shishigashira (Japan)
12. Pearlscale – Chinshurin (Japan) Chee-lun (China)
Phoenix Eggfish – Egg Phoenix (an Eggfish with a long, flowing and deeply forked caudal fin)
13. Pompom – Pom Pon, Pon Pon, Velvetyball Eggfish, Velvet Ball, Hanafusa (with dorsal fin)
14. Ranchu – Buffalo-Head
15. Ryukin – Onaga, Nagasaki goldfish (both antiquated)
16. Tamasaba – Sabao, Mackerel Tail, Yamagata Goldfish
17. Telescope-Eye – Globe Eye, Dragon Eye, Demekin
18. Tosakin – Curly Fantail, Peacock Tail
19. Veiltail – Philadelphia Veiltail, Oriental Twintail, Feather-Dressed Long Finned Man-yu
20. Wakin – Japanese Goldfish
Watonai – Long-Bodied Ribbontail (a cross between the Wakin and the Ryukin)
You can “Google” any of these names to see beautiful pictures and to learn more about them.
To “whiskyb”, your goldfish which you described as all red with a white face is most likely a Sarasa Comet, a variety of Comet which is red and white only.