Sodium transition metal layered oxides are a class of materials which exhibits fascinating properties, such as high thermoelectric power. Whereas most of the work conducted so far focused on 3d transition metals, mainly cobalt, compounds with 4d metals could be excellent materials to obtain new strongly correlated electron systems. This work is focused on Na xRhO2 compounds, with O3- and P2-type structures. The P2-type structure was obtained by ion exchange from the potassium phase P2-K0.62RhO2. This type of synthesis was conducted here for the first time on layered oxides with 4d transition metals. The phase diagram of both structures was explored by sodium electrochemical deintercalation/intercalation in a battery. The existence of single phases was shown with presumably different physical properties. As an example, the O'3-Na1/2RhO2 compound electrochemically obtained for the first time exhibits a metallic behavior, whereas the O3-NaRhO2 phase is a semiconductor. The synthesis of each single phase existing in both the O3- and P2-type systems should lead to new insights into the structure-properties relationships of this class of materials.