Pond Boss Forums FISH & FISHING Fly Fishing & Other Fish Species Koi, Gold Fish, & Israeli Carp

Goldfish generally grow to only 12"-14". Koi can get 28"-30" maybe more in optimum conditions. They are different genera but can hybridize resulting in fertile offspring as CJ says. I never saw one of these hybrids. Not sure about their maximum size.
Israeli and mirror carp are the same species.
From the web:
The difference between mirror and common carp is both genetic and visual - biologically they are similar. The mirror carp was the first mutation of common carp, owing to two alternative genes, the S allele and the N allele. The genetic term for a mirror carp is "ssnn" (all minor). Common carp have an even, regular scale pattern, whereas mirrors have irregular and patchy scaling, making many fish unique and possible to identify by sight, leading to most carp in the UK over 40lb being nicknamed. This lack of scales is widely believed to have been bred in by monks in order to make the fish easier to prepare for the table.
The shape of a Mirror Carp is different to that of a Common Carp. Mirror carp are generally having a fuller and more rounded shape. Some Mirror carp are rounded in the shape of a dinner plate. A large swollen belly is not uncommon in larger specimens. The colors in a Mirror Carp are dependent on the water in which it lives. Gravel pit carp can be almost black; Carp, which are found in clay ponds, can be a light gray or brown with large areas of red/Orange/Gold coloring.
The Mirror Carp is identified by irregular scales dotted haphazardly over its body. Anglers have subdivided the patterns of the scales into easily identifiable descriptive patterns. Fully-scaled Mirror Carps are completely covered in scales of different sizes. Mirror carp generally have a fuller and more rounded shape than Common Carp. A large swollen belly is not uncommon in larger specimens. The colors in a Mirror Carp are dependent on the water in which it lives. Gravel pit carp can be almost black, whereas those found in clay ponds can be a light gray or brown with large areas of red, orange or gold coloring.
Contrary to popular belief, Leather carp are not Mirror carp without scales; there is a distinct genetic difference. Leather carp are permitted a few scales; however, the dorsal row of scales is either absent or incomplete. Leathers also have reduced numbers of red blood cells, slowing growth rates. A perfect fully scaled mirror carp are completely covered in scales of different sizes.