Most "LiPo" batteries are typically the same chemistry as your "Lithium-ion" but without the puncture and pressure resistant casing. The plastic pouch is the "polymer" part. LiPo batteries are lighter and can produce more current than basically the same thing in a safer standard container.
So yeah, big difference in safety, not really a difference in the chemistry.
The above was explained to me by someone I believe knows what they're talking about. But I may have misunderstood; if I have, please let me know!