Battery capacity can be indicated by the multiplication of the discharge current and the time to reach discharge cut-off voltage.Battery capacity(Ah)＝∫I (t) dt
As far as the above formula is concerned, discharge time varies with discharge current, which means battery capacity varies with discharge current.
Take 20 hours and 1 hour for example:
20 hours,0.05C(A)×20(h)=1C(Ah)
1 hour,0.6C(A)×1(h)=0.6C(Ah)
That is to say, one-hour-rate discharge capacity equals to 60% of twenty-hour-rate discharge capacity. It also means with the increase of discharge current, the discharge capacity will decrease. So generally speaking, the discharge cut-off voltage also varies with discharge current.
Battery capacity is also affected by temperature during the discharging process. Generally speaking, battery capacity decreases as temperature falls. The discharge characteristic is shown as figure 1:

(1)The discharge characteristic at different rates
Figure 1 discharge characteristic at different discharge rate

figure 1 discharge characteristic at different discharge rate[20oC(68oF)]