With just that information a :
2S1P is a pack with (2) individual cells wired in series
2S2P is a pack with (2) sets of individual cells wired in series and then each set of (2) series wired cells are then wired in parallel.

If each cell in each pack has the same "C" rating and the same MAH rating then the 2S2P pack will provide double the capacity (MAH rating and "c" rating) versus the 2S1P pack. Example using a 3.7v 2200mah 20C cell: the 2S1P pack would equal 7.4v 2200mah 20C and the 2S2P pack would equal 7.4v 4400mah 40C.
If the packs are made to have equal "C" ratings and MAH ratings then the main difference between a 2S1P and a 2S2P would be weight as the 2S2P would be heavier. Example : a 2S1P pack rated at 7.4v 2200mah 20C would need (2) 3.7v 2200mah 20C cells and a 2S2P pack rated at 7.4v 2200mah 20C would need (4) 3.7 v 1100mah 10C cells.