3 Answers

Yes.  Carp and Goldfish are related.  Goldfish have been augmented to look the way they look for various reasons including bringing "Good Luck".  These varieties would not occur in the wild.  They are very susceptible to disease because of this.

Diseases in Goldfish can be common, contageous to other goldfish, and sometimes fatal. If the goldfish disease symptoms are seen early, and the correct goldfish disease treatment can be given quickly, most goldfish make a complete recover. Goldfish diseases diagnosis is an important part of the overall goldfish care. If you can't make a disease diagnosis see your local vert, or pet store.

While goldfish don't give disease to humans, like every other organism, goldfish can aquire them. Goldfish diseases cut short many goldfish lives because the owners did not know enough about goldfish diseases, how to diagnos these goldfish diseases, and finally how to deal with the goldfish disease treatment.

Please choose from the following Goldfish Diseases.

Anchor WormCostiaCotton mouthCotton WoolDropsyFinrotFlukesHole in the headIchLiceSwim Bladder DisorderTrichodinaVelvet

http://www.desktopgoldfish.com/goldfish-diseases.php

I worked with fish for years and I can tell you that every single disease listed above I have seen on other types of fish.

I agree with some, animal diseases are host specific, usually.  There are many diseases which may affect other species, maybe in a different degree.  But yes, diseases of aquatic species would more than likely be common to carp and most other fresh water fish, amphibians, and maybe even reptiles.  I would bet that big carp would devour the goldfish if they were introduced to the pond, within minutes, if not seconds.  Even if diseased, the ingested fish would then not be much of a threat to the carp population.  So, nature would probably keep a check on things with this food chain, survival of the species...

Goldfish are a Carp,