As for lithium battery and lithium ion battery (lithium polymer battery also belongs to lithium ion battery), lithium battery is a battery using lithium metal or lithium alloy as cathode material. The chemical characteristic of lithium metal is very active, so that the lithium metal needs very strict requirements on the environment for its process, storage and application. The cathode material of lithium ion battery is intercalated structure material such as carbon. Lithium ion battery is safer because just Li ion transmits between anode and cathode inside the battery. As for lithium ion battery and lithium polymer battery, the electrolyte of lithium ion battery is liquid state, while that of lithium polymer battery is gel or solid state, which make the battery safer.
The scientific name of lithium ion battery is lithium secondary battery, having corresponding cathode materials. Differed from primary lithium battery regarding lithium as one electrode, lithium secondary battery is liquid electrolyte which fuses LiPF6 and LiClO4 into the electrolyte of DMC:EC(v:v=1:1). Some electrolyte has modification, but lithium secondary battery is still a liquid battery.
In term of the inner materials of lithium polymer battery, its electrolyte is polymer, normally is gel electrolyte and solid electrolyte. South Korean has invents gel battery with PEO-ion as electrolyte. It is unknown whether there is this kind of battery in GalaxyRound or LGGFlex.
There are some differences on package between lithium polymer battery and lithium battery. Lithium battery has steel shell package (18650 or 2320), while lithium polymer battery packaged by aluminum plastic packaging film, which named pouch cell.
Some lithium battery has total solid electrolyte, such as LiPON, NASICON, perovskite, LiSICON, the ceramic electrolyte with high conductivity or glassy electrolyte made by amorphous substance. It may belong to lithium secondary battery.
All in all, lithium battery can be divided into two categories: lithium metal battery and lithium ion battery. Normally, lithium metal battery is un-rechargeable with metallic lithium, while lithium ion battery does not contain metallic lithium but is rechargeable. Lithium battery, lithium ion battery and lithium polymer battery has theoretical differences.