Normally equilibrium refers to a closed system without net heat transfer. Steady state  refers to a (potentially) open system where there might be heat transfer but no change of the state of the system.

your understanding of thermal equilibrium seems to be not correct. Consider 2 Systems which have different temperatures and which are connected to each other in that way that heat transfer can occur. Heat transfer can only occur when you have a delta T. if both systems have the same temperture (hence delta T is zero) no heat transfer can occur since there is no more driving force available => you have reached your thermal equilibrium. in steady state case for heat transfer you have stable delta T so that there is a constant heat transfer and constant temperatures.

For chemical reaction the equilibrium is reached when the A is converted into B with the same rate of reaction like B reacts to A, but that means not (neccessarily) that the concentration of A and B is the same like in the case for thermal equilibrium.

Take into account the definition given by Peter. The difference between steady-state and equilibrium is the type of system: open system (steady-state) and close system (equilibrium); and the exchange of mass or heat. An open system cannot reach the equilibrium. On the other hand, the steady-state can be reached by an open system when the input and output of mass or heat are equal.

Your statement is not clear:

In chemical equilibrium between A and B, there is the cases that A becomes B and B becomes A.(So there is transfer between A and B) but there is net change of extent in A and B (what this means?"

There is no transfer between A and B. A becomes B as the result of a chemical reaction.

Is it "Steady-state" or "Equilibrium"? - 

The concept of "steady state" belongs to chemical kinetics, while "equilibrium" to thermodynamics.  The steady state conditions commonly achieved in non-equilibrated systems. 

Equilibrium is a thermodynamic concept. A system at equilibrium has reached the minimum of a thermodynamic potential and therefore does not continue to evolve.

Steady-state is a kinetic concept. The composition of a system does not change over time because the effects of external exchanges and reactions in the system compensate themselves exactly.

As specified by Peter and Pedro, the concept of equilibrium refers normally to a closed system while the concept of steady-state refers normally to an open system.

In chemical kinetics, the term "steady-state" is sometimes used to refer to a state which is not. The simplest example is the reactions A-> X (R1) and X-> P (R2). One speaks of steady state if the concentration of X is given by the equality of the rates of the two reactions. We write dX/dt = k1 A - k2 X = 0 or k1 A = k2 X. However, in a closed system, the concentration of A always decreases, and therefore also the concentration of X. dX/dt is not equal to zero. k1 A = k2 X is an approximation and we should speak of QUASI steady-state.

Consider the industrial situation of a Continuous Stirred Tank Reactor for an exothermic reaction.  This has two (or more) inlets for two chemicals, an agitator and cooling jacket or internal coil.  The chemicals are pumped in at a constant rate, they react during the residence time and the mixture of products, reagents and solvents leaves at a constant rate.  The cooling system removes the heat of the exotherm. When working correctly, the outlet mixture is of constant composition and temperature.

This system is at steady state but not equilibrium.

Equilibrium by definition is the state of a chemical reaction in which its forward and reverse reactions occur at equal rates so that the concentration of the reactants and products does not change with time; An example of the equilibrium would be: A  B   when  µA = µB, or or Keq =  [A]/[B] …i.e. the concentrations of A and B are at their equilibrium values. 

An example of the steady state: the movement from A => X => B continuously; however, no changes occurs to [X] because X is formed from A as fast as it is converted to B, thus d[X]/d[t]=0. However, It is important to note that steady state approximation does not assume the concentration of reaction intermediate X to be constant (and therefore its time derivative being zero), it assumes that the variation in the concentration of the intermediate X is almost zero: the concentration of the intermediate is very low, so even a big relative variation in its concentration is small, if considered quantitatively.

I noted heare the difference between "Equilbrium assumption" and "Steady state approximation" based on chemical reaction system but is idential to heat transfer system, as you know.

I hope that you can understand your misunderstanding on "steady state of heat transfer".

To clarify this issue I suggest to consider the following definition given by Gibbs. Thermodynamic equilibrium of an isolated system is the condition wherein entropy has its highest value. This definition applies either in case of thermal or chemical cases.

As far as non-equilibrium stable states (thermal or chemical) are concerned, the isssue is not straightforward. In case of a system not far from equilibrium, a stable steady state can be defined as the condition corresponding to a minimum of entropy production (this latter being the derivative of entropy on time). When the system is far from equilibrium several stable steady states are possible, but the condition of their existence cannot be expressed by a simple principle as in the forehead cases. For this subject I suggest to refer to Prigogine.

One can in principle define an equilibrium state as a state with maximum entropy, but that requires a definition of entropy. The usual definitiion of entropy implicitly use the notion of entropy. To see this we note that entropy and absolute temperature are two concepts that are so closely related that if we have one of them one can easily define the other. That means that if one can define the entropy of a non-equilibrium system then one can also define a "global" absolute temperature of a non-equilibrium system. Now, it has turned out that it is very hard to define a global temperaure of a non-equilibrium system.

What can often be done is to consider a non-equilibrium system as composed of subsystems where each subsystem can be isolated and relaxed to equilibrium. Then the entropy of the whole system is defined as the sum of the entropies of the subsystems and each subsustem is assigned an absolute temperature, but the whole system is not assigned an absolute temperature.

As far as entropy is concerned, I would like to point-out that:

1. Entropy variation can be analytically determined only in reversible transformation. In this case Clausius’ Law dS=dQ/T is applied.

2. In case of irreversible transformations there is no analytical (exact) way to determine entropy variation. Adopting Prigogine’s convention, in this case Clausius’ Law can be written as dS=dQ/T+ diS where the latter term diS represents the irreversible contribution. The analytical form of this term is not known. The maximal information is that it is positive (as consequence of the second law). Consequently entropy variation in irreversible transformations can only be estimated using approximated models such as that mentioned by Peter.

3. HenceI agree that far from equilibrium entropy cannot be analytically determined. I also agree that far from equilibrium a system is not marked by a unique value of temperature. But nevertheless I don’t think that this latter point is the reason for entropy cannot be calculated at non-equilibrium. The ultimate reason is the inherent ignorance of irreversible term.