NHE: potential of a platinum electrode in 1 N acid solution
SHE: potential of a platinum electrode in a theoretical ideal solution (the current standard for zero potential for all temperatures)
A reversible hydrogen electrode (RHE) is a reference electrode, more specifically a subtype of the standard hydrogen electrodes, for electrochemical processes. Unlike the standard hydrogen electrode, its measured potential does not change with the pH, so it can be directly used in the electrolyte.
The name refers to the fact that the electrode is in the actual electrolyte solution and not separated by a salt bridge. The hydrogen ion concentration is therefore not 1, but corresponds to that of the electrolyte solution; in this way we can achieve a stable potential with a changing pH value.