Are the maximum battery voltage and the open circuit voltage (equivalent circuit ) of the battery the same?
If you model the battery equivalent circuit with Rint circuit, Are the maximum battery voltage and the open circuit voltage of the battery the same?

Yes. Because in open-circuit no current is flowing, therefore no voltage drop across the resistance. That means if you measure the terminals you measure the actual internal battery voltage.

And can we interpret the range in which the terminal voltage decreases due to the resistance of the circuit when the current flows as the available voltage range of the battery?

In part. Don't forget the battery voltage itself decreases as the battery discharges. So the open-circuit voltage itself decreases as the battery is discharged.