longhair, one lithium polymer cell (single unit of voltage source) is 3.7V. Two of them connected in series (2S) would give 7.4V. Two of them connected in parallel would give 3.7V but double the capacity (if each individual cell is the same.)

A 2S2P battery (a battery is more than one cell) is made up of four cells in series/parallel configuration. The 8000mAh battery you mentioned above would have four 4000mAh cells. Cell 'a' and cell 'b' would be connected in series to give 7.4V at 4000mAh capacity and the same will be done to cells 'c' and 'd' to give another battery of 4000mAh capacity at 7.4V. These two 7.4V batteries (ab and cd) are then connected in parallel to give one singel battery of 8000mAh capacity at 7.4V.

Wrt your post#3 question, besides capacity difference (hence runtime and current output,) there are no differences.

If you plan to run two bateries (same voltage and capacity) in series, just make sue they are balanced properly and that there is some sort of voltage cut off feature in your ESC or wherever that prevents the voltage from dropping below 12V (ie 3v per cell).