Power is a term used when there is an element of time. Capacity can be thought of as volume.
A commonly used test is the 30 second wingate test. You put a person on a bike and resistance is placed on the wheel. The person is told to go "all out" for 30 seconds.
At the end, you have a measurement of the amount of work done in joules. That is the capacity.
To get power, you take the joules and divide by time (30 second) to get watts (joule/sec).
Think of it as a tank of gas in a car. That gas has the capacity to take you for many miles, but you can also burn it off very quickly (power).