Since capacity is defined for cells it's calculation must adhere to
some standards for these parameters.
It is totally untrue. Batteries are designed for different purposes/uses. There are high-capacity batteries with moderate discharge rates (as for laptops). They have all electrode films thinner, so the active electrochemical surface per unit of volume is bigger, which gives higher overall capacity. But thin electrodes will have higher impedance, so overall battery's ESR is higher, and it can't deliver high currents without damaging itself. So the capacity is always defined at certain discharge rate AND for specified CHARGE conditions, which vary for different cells.
There are batteries designed to deliver high current, for RC models and drones, up to 50x-100x-150x of their "nameplate" capacity. So a cell with 1000mAh capacity can deliver 150A of current for drone motors, for example. But this battery has to have thicker electrodes to have low ESR, and thus they usually have somewhat less capacity per volume of the cell. More, usually these batteries are not expected to survive more than 50-100 recharge cycles, so they are operating under highly stressful conditions.
The recommended discharge cut-off is also determined by manufacturer, by their advertised (targeted) ability to take certain number of re-charge cycles. If the voltage cut-off is higher, and charging current cut-off is higher, the battery would last longer (however at somewhat smaller capacity), 1000 - 2000 - 5000 cycles, which you would want for some equipment and cars.
So no, there couldn't be any standards for discharge current and cut offs, these are individual parameters for individual products optimized for different purposes and manufactured with different technology implementations.