Are there differences between renal, hepatic, cardiac and kidney, liver and heart? Is the "jargon" used more commonly because of tradition, or is there some definitive biological basis to it?
Medicine is not my field, but I want to point out two things:
The former words have latin (or greek) roots, and historically latin was the international language of science. Therefore, nomenclature in different scientific fields are often based on latin.
The former words describe tissues and the related functions/processes (e.g. renal = kidney + related tissues + processes carried out by the renal system), while the latter are names of organs. Therefore, the former words are more suitable and precise when you want to describe these processes. For instance (as far as I know), Hepatic disease can be be caused by problems outside of the liver as such, e.g. blockage in the hepatic vein.
Users more knowledgeable in medicine are welcome to fill in or correct me if I'm mistaken.