I have been researching this for quite some time, and agree, its all terribly confusing.
There seems to be no consensus on what is best, but "best" depends on what you are trying to achieve.
Do you want maximum battery performance, and are prepared to accept a short battery life to get it, or do you want your battery to last ten or fifteen years ?
If its going into some high discharge hand held gizmo, you probably want maximum battery performance between recharges.
If its a $10,000 solar battery storage bank, you care less about performance and expect not to have to replace that battery after only six months of use.
Same (or similar) battery chemistry, widely different expectations.
What seems to be going on here, is that these lithium cells seem happiest at around 3.2 volts. They will last forever at that voltage, and it corresponds to about 40% to 50% of stored capacity.
They have negligible self discharge at 3.2 volts, and that is normally how they are supplied when you buy them.
Minimum voltage at end of discharge is about 2.9v to 3.0v depending on rate of discharge, anything less will reduce battery life. Every time you over discharge the battery it causes slight but irreversible damage and reduced capacity.
At the other end of the scale charging up to about 3.4 volts will be nowhere near full capacity, but the battery will last for years if you never charge beyond that.
Charging up to 3.7 volts will get you near maximum capacity, but it will cause an accelerated life reduction, and self discharge will also increase.
Charging at 4.2 volts is about the limit of useful capacity, but again it is a trade off of performance versus battery life.
It may be a good tradeoff for some small high rate of discharge application, where the batteries are taken straight off the charger and immediately used, and high self discharge from that elevated voltage is of no interest.
Over four volts you gain nothing in capacity but can seriously irreversibly damage the cells.
So what is correct ?
I really do not know, it depends on what you expect from the battery.
The wider the voltage swing either side of 3.2 volts the more you are punishing the battery, but the higher the performance will be, up to a point !
The hot tip seems to be not to float charge these cells.
Run full charging current up to the cut off voltage, then completely stop charging.
The cutoff voltage might be anywhere from 3.4 volts to 4.2 volts.
The battery manufactures know all this, but they also know that if they say charge to 3.4 volts, their battery capacity will be very poor and not competitive with competing batteries.
If they advise charge to 4.2 volts, their battery will have a huge capacity but will quickly die, but they never mention that.
If YOU were a battery salesman, trying to sell a lot of batteries, what would you advise ?