Nobody looks after their goldfish and everybody acts surprised when they die. Seriously, they are like all other fish, so they need clean water too. There are many variations of goldfish, like lion head goldfish, pearl scale goldfish, but they all have the same scientific name. The top photo is a black moor.
This photo is a fantail, I can't see the other half of the tail, though.
This is a fantail. Again, I can't see the double tail, but I know for sure that this one is a fantail.
This is a ranchu. Note the absence of a dorsal fin.
This one appears to be an albino black moor.
