Battery Capacity Rating
Batteries, especially older types like Lead Acid, can supply a certain amount of energy, which depends on the current drawn.

The internal resistance causes waste inside the battery, so at a very high current the energy that comes out in total is lower than at lower currents, because more "stays in the internal resistance". It also has to do a little bit with chemical reluctance, but we can leave that out.

Usually batteries specified at ##W over ##min are types that are meant for deep cycling and the number allows a designer to assume that energy over that timespan.

If you want you can convert that rating to an approximation of Ah by calculating the Wh and then dividing by the median battery voltage:

30min at 112W => 56Wh =(2.15V/cell)=> 56Wh / 12.9V =~ 4.34Ah (at 30min = 8.68A for 30min)

But the battery can easily be one that would be specified at 7Ah or even more, because normal (non deep cycle?) batteries are rated at 1/20th, or sometimes 1/10th) the current draw that is their capacity, so a 20Ah would be tested at 1A current draw. And as told before, the higher the current the less energy you can get out of them.