All goldfish are, after all, goldfish. No matter it's an oranda, bubble-eye, ranchu, ryukin etc they're all
Carassius auratus.
It's all in the
body morphology. We differentiate every breed of goldfish solely on the
morphological differences (and colouration of course) between each individual fish. We give them different names to differentiate between
"a set of characteristics" that each fish has eg. if a fish got a wen, a dorsal fin, and a double-tail, then it's an oranda.
Fantails and ryukins are completely different, u say? I'm not completely in agreement with the statement. After all, a ryukin is a fantail with a pronounced hump, simple as that. The hump can be big or small, but if it's pronounced enough, then it's a ryukin. Of course, a good quality ryukin will have a long line of selective breeding behind him with a long line of good quality ryukin parents to back him up, so saying a ryukin is a fantail with a hump is also not entirely correct. Ironically, if a pair of
champion ryukins with the perfect ryukin characteristics are to spawn, their spawn will
undoubtedly produce a mixture of fantails, nymphs & ryukins, and probably only very few handful will inherit their parents' perfect characteristics.
So, u ask what are the fish we call fantails? In my opinion, a fantail is a goldfish (Carassius auratus) that has these "set of characteristics": double-tail, dorsal fin, no hump, and a "clean" facial attributes (no wen, no telescope-eye, etc). What's a ryukin? A goldfish which has similar characteristics as above, only add "prominent hump".
My two cents