Just a note about the Central/South American cichids
. Many of these are also classified as New World Cichlids as well, such as the firemouth or dwarf. New world usually refers to the area Texas in the US and south through Central and South America. So if hear the term South/Central American cichlids used with New World Cichlids that is why, both are correct.
As well you may hear the term Old World cichlid used, this is generally refering to African Cichlids. (though to really confuse you some African cichlids are refered to as New World as I have found in several reference books)
The key to remembers is Cichlids are just about everywhere, In Africa in rivers, streams, in South America in the Amazon and permanent rain forest puddles, they have been spread by man accidently, or on purpose.
And some places they are food "Rio Grande Perch" AKA "Texas Cichlid" is often caught by fly fishing in southern Texas and yes some people eat it.