@DKNguyen, they are not. 4P16S is 16 packs of 4 cells connected in parallel. Than, you take the 16 individual packs and string them. The other one is 4 strings of 16 cells each, connected in parallel. It's Parallel First vs. Series First. When new, electrically it's the same. But failure modes are very different in case of cell failure.
Portable equipment needing higher voltages use battery packs with two or more cells connected in series. Figure 2 shows a battery pack with four 3.6V Li-ion cells in series, also known as 4S, to produce 14.4V nominal. In comparison, a six-cell lead acid string with 2V/cell will generate 12V, and four alkaline with 1.5V/cell will give 6V.
In a series configuration, the battery is as strong as the weak link in the battery chain, so the higher-capacity cell cannot charge more than the weaker cell. The weaker cell also discharges and charge first, which also cause a problem like over-discharging and over-charge in the device. The single-cell configuration is the simplest battery pack.
This can be purchased as a one off for $15 or get all updates for a year and access to the databases for $25. When designing a battery pack it is useful to make a few series and parallel calculations.
This combination of cells is called a battery. Sometimes battery packs are used in both configurations together to get the desired voltage and high capacity. This configuration is found in the laptop battery, which has four Li-ion cells of 3.6 V connected in series to get 14.4 V.
Such a configuration is called 4s2p, meaning four cells in series and two in parallel. Insulating foil between the cells prevents the conductive metallic skin from causing an electrical short. Most battery chemistries lend themselves to series and parallel connection.