A lithium-polymer battery (LiPo) is a rechargeable battery that, in the case of true LiPo, uses solid polymer for the electrolyte and lithium for one of the electrodes. Commercially available LiPo are hybrids: gel polymer or liquid electrolyte in a pouch format, more accurately termed a lithium ion polymer battery.
True LiPo batteries have not reached commercial viability. The batteries referred to as LiPo in commercial use offer reduced thickness, flexibility and weight.
Their qualities make LiPo batteries suited to thin smartphones, tablets and wearables. While LiPo made a splash in radio-controlled hobbies and still remain an option, LiIon (lithium ion) are making a return due to their better discharge abilities. While pouch-type standard LiIon batteries exist, they still require external casing to prevent expansion that would otherwise become a performance and safety issue.
Current LiPo batteries are actually more of a half-step away from LiIon batteries as they don't use a true lithium polymer solid, as the original Bell Laboratory designs of the 1970s had, because the solid polymers don't perform well at room temperature. Both battery types use the same materials for cathodes and anodes. The real internal difference between the two is that the insulator between electrodes is made of a micro-porous polymer in LiPo rather than the traditional porous film separator used for LiIon.
The choice between LiIon and LiPo depends on the application its being chosen for. Today’s LiPo batteries have a shorter shelf life but a longer self-discharge time. Longer self-discharge makes them better for devices that might sit unused a few days here and there. LiPo also have a leg up in fitting tiny and slim forms.
On the other hand, LiPo have worse low-temperature discharge (0'C to 60'C) than traditional LiIon and discharging LiPo batteries to ultra-low voltages can be dangerous. Deep, fast discharges may cause expansion, combustion or even explosion. LiIon cells have better performance for very high-drain uses. Both LiPo and LiIon batteries require special smart chargers and often require circuit protection for the safest use.
Gamers Nexus compares battery types: