I'm not sure what you mean by mentioning a "12V Li-Ion".Wenn 14.4v LiPo geht, dann geht 12v Li-Ion auch.
Some battery theory for whoever is interested
Lithium-ion polymer (LiPo) and lithium-ion (Li-Ion) cells have the same "nominal voltage", being 3.6 or 3.8V. Main difference as far as I know is the electrolyte, which makes the LiPo a bit more versatile (can deliver higher current, less delicate) but also less dense (and a bit heavier).
All these cells start at 4.2 (LiPo/LiIon) or 4.4V (LiHV, a LiPo with slightly different chemicals - for all types: always respect the maximum, don't overcharge!) and they are "empty" at 2.7-3.0V (I usually just see 3V as the bare minimum).
The voltage of the battery pack is determined by the amount of cells connected in series; high-current battery packs usually have a lot of cells in parallel. Most packs will be specified for this: mine are all 3S (3 cells in series, so 3S, and because there are only 3 cells in the pack there is nothing in parallel and they are 1P, which is then usually omitted).
So the voltage for 1 up to 6S is calculated by multiplying the nominal voltage with the number of cells: 3.6 - 7.2 - 10.8 - 14.4 - 18.0 - 21.6
Or sometimes: 3.7 - 7.4 - 11.1 - 14.8 - 18.5 - 22.2
On my batteries, this means a full battery will always give me 12.6V, except for one LiHV pack (lithium high voltage) which starts at 13.05; when they're "empty" they have 9V left in them. Most of my packs are rated at 5000 mAh and they perform quite well because my charger registered 5625 mAh of power going in today (charging from 2.98 - 3.01 - 3.00 all the way up to 4.2 in all cells); over 10% more than the rated capacity (so 9V is really "empty").
So your "12V Li-Ion" is probably a 3S setup (starting at 12.6V and empty at 9V), while a 14.4V lithium polymer is probably a 4S (that starts at 16.8 and stops at 12V).
If you're really in trouble and need to get home, you can keep a LiPo connected below 3V/cell (I've been told doing this with a Li-Ion can be dangerous), but keep in mind you will probably kill the battery pack by doing this one or at maximum a few times. I have one old pack here from the QV that I did this to (because I was riding home and there was storm and lightning), but after only one time this packs capacity went down from 5000 mAh to about 3200.
Concerning power delivery, might be funny to know: I have one 3S2P battery pack, and it's rated to be capable of 90C for a short period of time (I believe the manual said 10 seconds). If you have a car and you ever have a flat battery, just grab and connect this with a fat cable because these small lithium polymer packs are easily capable of starting it. The "90C" rating is linked to the capacity: Multiply the number before the C with the capacity in Ah and you have the maximum current in A that this battery can deliver. This is a 6000 mAh = 6 Ah battery pack, so for a short period of time it can 540 amps. Heck, you can start 4 diesel engined cars at the same time with the current