How much current does a battery store?
A figure like 550 A means that the battery is capable of supplying a total of 550 amperes for a short period of time like a quick triggering of the car starter. Now, if you only draw 1 A out of a 55 Ah battery it will be able to supply the current for a total of 55 hours. Likely, if you draw 2.75 A it would last (55/2.75 = 20 hours, regardless of voltage.    

The figure amp-hour (Ah) is a product of the amount of charge available in the battery. Charge like in coulomb or electrons. Since 1 ampere equals 1 coulomb during 1 second then the ampere measurement is the rate of charge flow per unit of time. Then the product of (charge count)/time  X time = (charge count) you end up with your figure of amp-hour turn out to be how many coulombs is available in your battery. Why manufacturers don't express the battery capacity in coulomb is beyond my comprehension, but on a scientific standpoint that is what it is.    

One should not confuse ampere x hour (Ah) with the available energy. Both are interrelated but the later involve the voltage. The product of charge count x voltage is a representation of energy. Hence, if you have a 12 V, 55 Ah battery, the total energy available (theoretically) would be 12 V X 55 A X 1 hour = 660 watt-hours = 0.66 kWh of energy. Or, also 2.38 mega newton-meters or 568 kilo-calories or 1.75 mega foot-pounds. Something to ponder on. :)