A first note. I have an XTAR VP2 charger with a 3 way switch labelled: 3.2 3.6 3.8. This is a fine charger, but I wish the switch was just labelled with the target voltage when fully charged.
But this is getting off topic. Apparently 3.6 and 3.7 volt ratings are nominal voltages and apply to LiMn and LiCo cells. Both of these should be charged to 4.2 volts. The ratings are a bit of "specsmanship" on the part of manufacturers. Some newer construction have lower internal resistance and may yield closer to 3.7 volts at the 50 percent discharge point (which is where the nominal voltage comes from).
The 4.35 volt rating (and there are also 4.4 volt cells these days) is achieved by surface coatings on the electrode, and additives in the electrolyte. These cells are said to have a shorter life. I simply charge them to 4.2 volts (which is fine and safe), accept a loss of capacity, and hope for longer life.
Some people though say that the 3.6 volt specification pertains to older LiCo cells, which were charged to 4.1 volts whereas the 3.7 volt specification pertains to newer LiMn cells, which get charged to 4.2 volts. These sorts of batteries are not widely produced anymore and you are unlikely to encounter them. Saft still makes such batteries, but they are found in aerospace and military applications.
However, what many people refer to when they talk about LiPo batteries is high current output RC batteries. This are typicaly soft construction, but allow extremely high current output (on the order of 20C).
To add to the confusion, my IMAX B6 charger allows for 4 different Li-ion cells in the following way:
Tom's Battery pages / tom@mmto.org