I was looking at a couple of LiPo batteries and seen that there is a "2s" and a "2s2p".

What is the difference between the two and how important is it?

The LiPo's will be used in a brushless ground system if that makes a difference.

2S means two cells in series to make up the battery. Sometimes to get more capacity they would put two of these in parallel making 2S2P. Lots of us use the 2S packs for smaller planes, then connecting them in parallel for more capacity for larger planes. If you buy it as a 2S2P you can't easily go back to 2S. I nice paralleling adapter can be made from Deans Ultra plugs.

I'm a bit confused probably because the information is way over my head

To dumb the question down to help me get the answer I am looking for...

Other than the actual run time because of the mAh difference, will the following batteries work the same?

Lipo 5000HV 2S 7.4V Pack
[ul][*] 5000mah Capacity [*]7.4 Volts [*]45mm X 138mm X 18mm [*]20C Constant(100 amps) [*]30C Sustained(150 amps) [*]50C Burst(250 amps)
[/ul]

Lipo 8000HV 2S2P 7.4V Pack
[ul][*]8000mah Capacity[*]7.4 Volts[*]44mm X 137mm X 26mm[*]20C Constant(160 amps)[*]30C Sustained(240 amps)[*]50C Burst(400 amps)
[/ul]

Yes. In a perfect world you would get twice the endurance or twice the discharge rate of a 2S pack. In the real world it never quite works out that way. As long as your packs are of the same mah rating they can be paralleled. It's usually safe if they are also the same brand.
Walt

I plan on using the same brand and mah rating when I purchase them.

I'm planning to run them in series, so would that make a big difference when it comes to safety?

To the best of my knowledge there is no saftey issue in running LiPos in either series or parallel. I would keep a careful eye on the balance, however.
Walt

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).