Lithium ion batteries were developed in 1970s and were commercially available in late 1990s, lithium polymer batteries were developed in the 1990s. With the development of Li-ion batteries, they became very common in mobile electronic devices because of its small size and no effect on memory. Li-polymer batteries do not have same capacity as lithium ions and have even smaller size than Li-ions. Both Li-ion and Li-polymer batteries are rechargeable i.e. secondary batteries and are costlier to manufacture than standard rechargeable batteries.
Lithium ion batteries use carbon anode and lithium cobalt oxide cathode and an electrolyte gel. Chemistry of lithium polymer is much similar to Li-ions but it also uses a porous separator which converts into gel on exposure to electrolyte. Also Li-polymers employ different architecture. These batteries do not use metal shell like Li-ion batteries. Li-polymer battery is in next level of development and replaces liquid electrolyte with a plastic or polymer electrolyte thus allows these batteries to be molded in various shapes and sizes. The chemical construction of Li-ion battery restricts it to only rectangular shape.
Li-ion batteries have a major problem overheating due to which it has an active protection circuit which prevents overheating of the battery and bursting into flame whereas Li-polymer batteries do not require such protection circuit which makes its size smaller and easy to manufacture. Li-ion batteries are susceptible to degrade at the point they are manufactured and become dead in two to three years if they are not used. Li-ion batteries carry advantage of size, weight, energy density, ability to work in wider temperature range and that they can be recharged before getting totally discharged which any effect on memory. The initial voltage of Li-ion polymer battery is superior to standard Li-ion.
Li-ion batteries have a lot more energy capacity than that of Li-polymer batteries so Li-ion batteries are used in deices which have higher current requirement. Lithium polymer batteries are preferable where size is paramount. And when cost is considered, Lithium ion battery is the choice as they are cheaper to manufacture than Li-polymer battery. Li-ion batteries are used in applications like mobile telephones and mobile computing devices whereas Li-ion-polymer batteries are used in area where battery should be of any particular shape, preferable for pocket devices.