What S and P counts actually mean
A single lithium cell produces roughly 3.7V nominal (fully charged around 4.2V, considered depleted around 3.0V), which is rarely enough voltage or capacity for a robot on its own, so cells are wired together into packs. The notation 3S 4000mAh 25C on a battery label packs three separate pieces of information into a few characters. The 'S' number is the series count, how many cells are wired positive-to-negative in a chain to add their voltages together. A 3S pack has three cells in series, giving a nominal voltage of about 3.7V times 3, or 11.1V (fully charged closer to 12.6V). Series wiring is how you get from a single cell's ~3.7V up to the 7.4V, 11.1V, 14.8V, or 22.2V you commonly see on robot batteries, corresponding to 2S, 3S, 4S, and 6S packs.
The 'P' number, when present, is the parallel count, how many of those series strings are wired side by side to add their capacities together without changing voltage. A 3S2P pack has two parallel strings of three series cells each, doubling the capacity of a single 3S string while keeping the voltage at 11.1V. When no P number is shown, as in a plain '3S' label, it's understood to be 1P. The capacity number, given in milliamp-hours (mAh), tells you how much charge the pack can deliver, roughly how long it can sustain a given current draw, and directly scales with the P count and with each cell's physical size.