Things called "LiPo" or "LiOn" do not exist.
There is only lithium ion (li-ion) (rechargeable), which is sometimes also called "lithium polymer" as an industry inside joke. Polymer refers to the plastic vacuum pack enclosure. They actually tried to design a polymer-based electrolyte in late 90's, it never worked out but marketing wanted to still use the cool name! See how funny it is?
What you describe is all the same, and only being one single thing, has one set of lithium ion regulation, regardless of whatever the marketing people is calling it this year.
Then there is lithium metal (non-rechargeable), which is different, has completely different danger mechanisms, and may (or may not) have somewhat different regulations.