Why do different C-ratings show different capacities for the same battery?

[why does battery capacity change with discharge rate] Two reasons. Discharge rate: slower discharge extracts more energy, so C₁₀₀ capacity exceeds C₂₀ exceeds C₁₀. And cut-off voltage: the same battery quoted to 1.75 V per cell and to 1.80 V per cell shows different capacities. Compare batteries only at the same rate and the same cut-off. Example: a cell rated 1000 Ah at C₁₀ may be rated 1200 Ah at C₁₀₀.