There are a myriad of different lithium technologies now, and some of the new lithium batteries use hybrid technology to take advantage of different types.
The Lithium battery types are:
Lithium Cobalt Oxide(LiCoO2) — LCO
This is what is in your cell phone. It has the highest energy density, which makes it good for small batteries, but it has a short life span, low thermal stability and limited load capabilities (which is not a problem for cell phones but would be a huge problem for powering a high current inverter)
Lithium Manganese Oxide (LiMn2O4) — LMO
Used for power tools and some electric and hybrid cars. It has higher current capacity than LCO, but shorter life and lower energy density.
Lithium Nickel Manganese Cobalt Oxide (LiNiMnCoO2) — NMC
New hybrid technology used for power tools, e-bikes, and medical equipment. Excellent life (duty cycle in the 1000s), high current, and although safer than LCO, it is susceptible to thermal runaway. Not readily available for consumers yet.
Lithium Iron Phosphate(LiFePO4) — LFP
Used in some powersports and automotive batteries. It has a long life if not abused (duty cycle in the 1000s), high current, flat voltage discharge and is very safe and relatively inexpensive compared to other lithium technologies, but has low energy density and high self discharge. It is sensitive to cold temperatures.
Lithium Nickel Cobalt Aluminum Oxide (LiNiCoAlO2) — NCA
Used by Panasonic and Tesla. Has high energy density and longer life than NCO, but the same safety issues as NCO (e.g. self destructing Teslas).
Lithium Titanate (Li2TiO3) — LTO
LTO technology has actually been around since the 1980s. Used in solar powered street lights and other applications that require long life. Has extremely long life, but extremely high price to go with it. Can charge very quickly, has high load capacity, excellent cold weather performance and is extremely safe, but has a low energy density and as mentioned above is very expensive.