The difference between Lithium-ion batteries and Lithium Polymer batteries lies in the material used as the separator. Rather than an inert substance with holes covered in electrolyte, the separator is made of a micro-porous polymer covered in an electrolytic gel that also serves as a catalyst that reduces the energy barrier in the chemical reaction between cathode and anode. Therefore, Li-Polymer batteries allow for a slight increase in energy density. However, this advantage is offset by a 10% to 30% cost increase. Therefore, because the same materials are used for cathode and anode, Li-Polymer batteries follow the same chemical process as Li-Ion batteries and so are not a distinct class.
Because the solid polymer is flexible, it is possible to construct flexible batteries and batteries that can be easily formed into various shapes and sizes, even thin films. So you'll most often see Li-Poly used for batteries which are relatively thin (e.g. Nokia's 'hero' BP-4L battery used in a dozen devices) or oddly shaped (e.g. to fit round other components in a tightly packed phone).
Just as with Li-Ion batteries though, Li-Polymer batteries are slowly degrading from the day they are created, and are subject to the same harm caused by deep-discharges.
The faster you charge a lithium battery of any kind the less charge it takes which is obviously reflected in the runtime and its life-cycle.
The world's APV scene is designed around the basic dimensions and circuitry of Li-ion batteries.
Compared to the lithium-ion battery Li-poly is less advantageous in terms of life cycle degradation rate.
Lithium polymer-specific chargers are required in order to avoid fire and explosion.
Explosions can also occur if the battery is short-circuited, as tremendous current passes through the cell in an instant. Radio-control enthusiasts take special precautions to ensure their battery leads are properly connected and insulated. Furthermore fires can occur if the cell or pack is punctured.
Although very similar, I'm not sure the vaping world is for ready Li-Po batteries just yet.
Maybe next year if nanowire battery technology continues to advance as it has done the last two years.