Nope! Lithium polymer batteries are substantially different from lithium ion. Each generation of lithium batteries is a pretty unique chemistry, the only thing that stays constant is the use of lithium as the cathode. Electrolyte, anode, and interface chemistry actually progresses pretty quickly.

Also, for drastically different battery chemistries which have been commercialized, see sodium ion batteries, and to a lesser extent NaS/ZEBRA batteries.

**edit: typo