Well technically the batteries we use and know as LiPo's are not really Lithium Polymers. A true Lithium Polymer uses a polymerized electrolyte to prevent leaking which gives very flexible manufacturing capability as they can be custom shapes and very flat.
What we use is really a Lithium Ion in a plastic pouch where the term polymer refers to the plastic that the pouch is made from, the inside is a regular Lithium Ion technology.
So what you call it is up to your preference. You could call it LiPo, LIP or even Lipoly but it is really Li-Ion