In electrolyte concentration cell:
This question has multiple correct options.
A. The electrode material and the solution in both half-cells are composed of the same substances.
B. Only the concentrations of the solution of the same substances is different
C. $E_{cell}^ \circ = 0$
D. The Nernst equation reduces to ${E_{cell}} = \dfrac{{0.0591}}{n}\log q$ at 25°C.

Hint: Electrochemical cell has two types of concentration cells: electrolyte concentration cell and electrode concentration cell. Since the two half cells contain the same electrode and electrolyte therefore, $E_{cell}^ \circ = 0$ .let us discuss both the concentration cells in detail.

Complete step by step answer:
Electrolyte Concentration cell comprises two same electrodes that are dipped in an electrolyte which possesses different concentration levels. An electrolyte has a tendency to diffuse from a solution of higher concentration level to a solution of lower concentration level. Hence we get to know that both the electrodes in this are the same in type but the concentration of ions in them are different. The emf is given by
$E = \dfrac{{0.0591}}{n}\log \dfrac{{{C_2}}}{{{C_1}}}$
In an electrolytic cell the electrode material and the solution in both half cells are composed of the same substances. For example, Copper is dipped in a copper sulfate solution.
Hence the option A is correct.
Also we can conclude that though the concentration of the electrodes are the same but the concentration of solution is different. Hence option B is correct.
Let us now analyze the third option, If $E_{cell}^ \circ = 0$, $E_{cell}^ \circ $ is the standard electrode potential developed when a metal is in equilibrium with a solution of its own ions under standard condition and if the same metal is placed between the half-cell then the electrode potential becomes zero, hence $E_{cell}^ \circ = 0$ which is why option C is correct as well.
Since $E_{cell}^ \circ $ is zero when the same metal is placed between the half-cell, then
${E_{cell}} = \dfrac{{0.0591}}{n}\log q$, the concentration term is denoted by q at 25 degree Celsius or 298k. we know that the Nernst equation at 298 k is given by
${E_{cell}} = E_{cell}^ \circ - \dfrac{{0.0591}}{n}\log q$(where q is the reaction quotient)
And $E_{cell}^ \circ = 0$

Therefore option D is correct.

In a concentration cell, there are two electrodes that are involved. These are known as the anode and the cathode, or the left and right side, respectively. The anode is the side that is losing electrons (oxidation) while the cathode is the side that is gaining electrons (reduction).
Electrode potential is the potential that occurs when the metal is in equilibrium with a solution of its own ions. If it is under standard conditions, the standard electrode potential occurs in an electrochemical cell say the temperature = 298K, pressure = 1atm, concentration = 1M. The symbol ‘$E_{cell}^ \circ $’ represents the standard electrode potential of a cell.

Hence all the options are correct.

Note:
Electrode concentration cell is exactly opposite to electrolyte concentration cell, it has the same concentration of electrolyte in both the cells whereas electrodes have different pressure and concentration.