I'm no battery expert, but I'll see what I can do to help by explaining the 4 types of batteries PureSmoker sells:
The RCR123a batteries are 3v each and are used in the Prodigy V3 (2 stacked for 6v). They are a safer chemistry than Li-Ion called LiFePO4. These batteries reportedly will not vent or explode, as has been reported in other types of batteries.
The green batteries are your standard Li-Ion 3.7v batteries and are used in the Icon. These are non-protected, and there is still a big debate going on between protected versus non-protected. I won't really step into those waters except to say I, personally, have never had a problem with them. But take that for what it's worth: practically zilch. I just simply don't know enough about batteries to intelligently wage one argument over the other.
The orange/red batteries are also 3.7v and are also used in the Icon. But they are a safer chemistry than the regular green ones, called IMR. These are high-drain batteries that can much better handle the drain of low resistance cartomizers. These are all I use anymore since I use low resistance exclusively at 3.7v.
The last battery on their page is a 17670 3.7v battery and is used in the Prodigy V3 if you want to use it as a 3.7v device. This is a protected battery.
Finally, regarding folks running their V3 at 5v: As far as I know, the only way to do that is to use a custom-built 5v battery that some vendors (not PureSmoker) sell. In reality, these batteries are smaller cells that have been wrapped together in sequence to get a total of ~5v. I tried one and had no luck with it working in my V3. But others reportedly have. However, my bigger cause of concern was the fact that this battery got HOT (and I do mean HOT) while it was charging. That worried me, so I have not tried it again.
I hope that helped. Maybe someone with much more knowledge of batteries can fill in some of the gaps I left, especially in the protected vs. non-protected schools of thought.