Capacity:
An 800mah capacity pack will let you pull 800ma for one hour.
A 1600mah capacity pack can pull 800ma for 2 hours.

Rate:
A battery rated to pull 800ma can pull 800ma for an hour.
A battery rated to pull 800ma can pull 5 amps for a few minutes before overheating and puking its guts all over the receiver box.
It's probably exaggerated, but hopefully you get the idea.