Lights

Having taken one of the 4 cell packs apart they are configured 2 x 2.
I would say that the maths are correct in that the total battery capacity is 4 x 1 cell mAh. They are standard capacity batteries. i.e around the 2200 mAh range.

But if you put two batteries in series, you get twice the voltage, but the same capacity no?

An excellent intro to 18650 cells, their performance vs the capacity on the label, and a warning about "recycled" cell not marketed as such

Battery configurations are described as *{x}S{y}*P, where xy is the total number of cells, x is the length of each series and y is the number of series connected in parallel.

The series length determines the battery voltage, whilst the number of parallel sets determines the capacity at battery voltage

tl;dr:

Your 2S2P battery should be 4400mAh at (assuming LiCoO2 chemistry) a nominal 7.4V, providing 8.4V when fully charged and 6.4V in a "sensibly empty" state.

Running 18650s down to 3V per cell is possible, but you don't gain much runtime (pretty much falls off a cliff at 3.3V), and Li-ion rechargable batteries provide more total runtime over their lifetime if you recharge at about 20%.

You'll also get better runtime and more chargecycles by not running them too hard. Operating current (and charging current) is normally expressed in "C"s, where running a 2200mAh cell at 2200mA current is a 1C rate. Given a hypothetical LED lamp rated at 20W with a buck driver configured to supply the LED with constant current given a 6-9V input, you would need 2S to provide the necessary voltage, but with only 1P your cells would be pushing about 3A, or about 1.5C. With a 6-cell battery, 2S3P, each cell would be running at 1A, 0.5C.

The test results in Torchy's article(^) show 90%+ of rated capacity for good 18650 cells at 1A.

Batteries for RC models can be rated at up to 90C constant, but you wouldn't expect them to last many charge cycles