For a battery pack, the voltage, capacity, and discharge current capability are important for specs, and the type of cells, pack configuration, and construction are important physical specs.
15Ah combined with the voltage, 48V, provide the amount of stored energy and therefore range; so 15x48 = 720Wh or stored energy. The discharge current capability is measured in amps (A), represents the current that the pack can provide continuously, when combined with the voltage, provide how much power the pack can provide, so if the pack has a current capability of 30A, the pack can deliver 48x30 = 1440W.
In an example where both the 20Ah and 15Ah packs are constructed with same cells, then the 20Ah pack will have a higher discharge current capability than the 15Ah pack by 20/15 = 1.333. This is because the pack must have more cells in parallel to result in the greater capacity, and those additional cells increase the discharge current capability in addition to increasing the stored energy (this is where pack configuration and cell type come into play).
So using the 20Ah and 15Ah packs as an example, made of cells that can store 2500mAh, or 2.5Ah each and the ability to discharge at 5A, you can determine the pack configurations as 13S8P and 13S6P respectively.
13S means you need 13 cells in series to achieve 48V nominal. 8P and 6P results in 8x2.5 = 20Ah and 6x2.5 = 15Ah.
Current discharge current capability, similarly results in 8x5 = 40A discharge current capability and 6x5 = 30A discharge current capability.
So, the most important thing to look for in a battery pack is the cell type used and the pack configuration. Everything else is just math.