"Lithium polymer" is a marketing term. It doesn't have any technical meaning. It is sometimes, but not always, used to describe pouch cells. Pouch cells designated as either "li-ion" or "li-poly" have no difference.
There are other chemistry differences, though. Always refer to the correct datasheet of the exact product - if available, of course.
You do not need to maintenance charge li-ion cells. For best lifetime, keep at between 30-50%. Ignoring LiFePO4, in voltage, that would be roughly around 3.50 to 3.70V, depending on chemistry. 3.6V never goes wrong. At that state-of-charge, they won't practically self-discharge unless they are faulty. Maybe you can check the voltage every 2-3 years.
NiHaoMike's 3.85V is on the high side but really it doesn't matter that much, especially if he stores the cells in a refrigerator. Avoiding >3.9V and avoiding hot places is usually enough.
On the other hand, if they have a poorly designed permanently connected protection circuit pulling significant current, you may need to check the voltage periodically (like twice a year) and recharge if necessary.