Part of the problem is that we're still using nomenclature that dates back to when one had to parallel sets of LiPoly cells together to get acceptable discharge characteristics for the airplanes/cars we were using them in when they were first introduced to modeling (about 15 years ago). It was not uncommon then to have a pack that was described as, for example, "3s2p" which was a six cell pack with two strings of three series cells in parallel with one another. Now you mostly see "1s", "2s", "3s" and so forth and that's just one cell, two cells (in series), three cells (in series).
Using the same sort of nomenclature, a nominally 12V lead-acid battery is a 6s battery, or the 4 AAs in an Estes Electron Beam launch controller is a 4s pack of alkaline cells.
LiPolys are nominally 3.7v per cell though they are actually well discharged when down to that voltage at rest. A full cell is 4.2V, so a 2-cell pack ("2s") will be 8.4V when fully charged. You can see, then, how 2s packs get substituted for "9V" transistor radio type batteries (which are internally 6 tiny alkaline cells in series). And you can see, then, how a 3-cell pack ("3s") can stand in for a 12V battery in a launch system (or a jumper pack for your car) with a fully-charged voltage of 12.6V. Recent ones have such a low internal resistance that they don't sag much under load and so can deliver LOTS of current. This is another reason why a small LiPoly pack works well in dual-deploy sort of application.
But when they first became available, their internal resistance was quite high which is why they were paralleled. One of my first big LiPoly packs for an RC airplane was a 4s3p pack (3 strings of four series cells in parallel). It was as large and as heavy as the 14-cell NiCd pack it replaced, but it had FOUR times the capacity and therefore four times the flight time. This was for an airplane power system that drew around 30A at full throttle.
You also see them rated in terms of "C" - as in "20C". That means the cell can safely deliver current of 20 times the rated capacity number. A simple example - a 20C 1000 mAh (1 Ah) pack can deliver 20A (20 times 1A) without significant cycle life reduction. That also means you can discharge it in 3 minutes (1 Amp-hour - or 60 Amp-minutes/20 Amps = 3 minutes).
Clear as mud?
Another thought: It is painfully common to see the units of capacity (milli-ampere-hours - mAh) or ampere-hours (Ah) used interchangeably with current (mA or A) when talking about chargers in particular. It's just sloppy and I don't know how it got that way, but it has. It's just the same as confusing total impulse of a motor with thrust, and just as wrong.