It is unfortunate that the common vernacular for battery capacity speaks in terms of ampere-hours. To state that any given battery is a "44 ampere-hour" device is meaningless without also citing the rate in amps (or the interval of time) that the discharge test occurs. I'll refer you to an exemplar data sheet on a sealed lead acid battery:
http://tinyurl.com/35464p4
In particular, check out the plots in the figure titled "Duration of Discharge vs. Discharge Current". EVERY battery of any technology produces such a plot. Further, be aware that this family of plots assumes some nominal battery temperature . . . typically room temp or about 20C. Cool the battery off and the curves move down. Warm it up and the curves will move up. Note that the battery in the data sheet is "rated" as a 33 a.h. device. In the curve I cited above, and the data table on the left we see that the 33 a.h. capacity is realized if the discharge is carried out at 1.65 amps over a 20 Hour period of time.