Capacity is a measure of stored power, current is a measure of how fast the store can be emptied. In general you should use the capacity figure but keep the current below the maximum rating.
Treat that battery as having 2800mAh capacity with a discharge time of 2800/500 = 5.6 hours at no more than 500mA load. You have to respect that no matter what the capacity is, there is another limit to consider. For example, you couldn't say a 2800mAh battery could produce 100 Amps for nearly 2 minutes because although the calculation works OK, the battery would melt!
Brian.