In a few words, these three potentials are:

• Standard cell potential: the theoretical Nernst potential for a redox reaction, when the activities of all the reactants and products are one (hence standard)
• Equilibrium potential: the potential of the cell taking into account the activities according to the Nernst equation
• Open circuit potential: the experimental potential observed at zero current; it may show contribution from different processes, therefore it doesn't necessarily correspond to any fixed equilibrium potential value. Plus, it can change over time as the conditions in the cell change.

Quite briefly, the equilibrium potential and the standard potential are potentials that arise from thermodynamic considerations.  The phrase "open circuit potential" (OCP) means the voltage of the electrode is measured against a reference electrode using a high impedance voltmeter so that no current flows between the electrode in question and the reference electrode.

The voltage that is measured at open circuit could be the equilibrium potential, or it may be a different type of potential called a "corrosion potential" or "mixed potential".  (To make it more confusing, often when the phrase "OCP" is used, it is implied that a mixed or corrosion potential is what is measured).  To tell if the OCP is a mixed potential vs. an equilibrium potential, you have to understand the theory behind these two different potentials.

The classic text "Electrochemical Methods: Fundamentals and Applications" by A. Bard and L. Faulkner gives a thorough discussion of the standard potential and equilibrium potential.  For discussion of the theory of mixed (corrosion) potentials, a good corrosion textbook would be useful.  If you can find "Electrochemical Techniques for Corrosion" , edited by R. Baboian (a NACE 1976 Symposium volume);  the first contribution within, "Electrochemical Nature of Corrosion", by S. Barnartt gives a good overview of the theory.  Another book that may be useful is "Electrochemical Techniques in Corrosion Science and Engineering" by R.G. Kelly et al.

In a few words, these three potentials are:

• Standard cell potential: the theoretical Nernst potential for a redox reaction, when the activities of all the reactants and products are one (hence standard)
• Equilibrium potential: the potential of the cell taking into account the activities according to the Nernst equation
• Open circuit potential: the experimental potential observed at zero current; it may show contribution from different processes, therefore it doesn't necessarily correspond to any fixed equilibrium potential value. Plus, it can change over time as the conditions in the cell change.

-Equilibrium potential: Kinematic 

The electrode potential, E, of a metal refers to the potential difference measured (in volts) between a metal electrode and a reference electrode.

Ee is the equilibrium potential (or reversible potential), which describes the equilibrium between two different oxidation states of the same element, at whatever concentration (or pressure) they occur. Ee varies with concentration, pressure and temperature. It describes the electrode potential when the components of the reaction are in equilibrium. This does NOT mean that they are in equilibrium with the standard hydrogen electrode. It means only that the reaction components are in equilibrium with each other. In the reaction

Az+ + ze- = A,

-Standard cell potential: Thermodynamic 

The cell potential, Ecell, is the measure of the potential difference between two half cells in an electrochemical cell. The potential difference is caused by the ability of electrons to flow from one half cell to the other. 

The standard cell potential (Eocell) is the difference of the two electrodes, which forms the voltage of that cell. To find the difference of the two half cells, the following equation is used:

EoCell=EoCathode−EoAnode

OCP: Thermodynamic 

In cells where an electrode undergoes uniform corrosion at open circuit, the open circuit potential is controlled by the equilibrium between two different electrochemical reactions. One of the reactions generates cathodic current and the other generates anodic current. The open circuit potential equilibrates at the potential where the cathodic and anodic currents are equal. It is referred to as a mixed potential. If the electrode is actively corroding, the value of the current for either of the reactions is known as the corrosion current. large value of impedance or current equal zero. 

Jason , Antonio, and Kaveh, thanks for sharing your interpretations that was really helpful.

Juan Casado, I see you look professional, but your comment doesn't, So, I hope in future you be able to match these two, which would be helpful for you. Regards

Reza

Good source is Handbook of Batteries Linden and Reddy

Thanks Francis, I will look it up