Lithium battery is seen common, and where you heard it firstly?
Lithium-ion is named for its active materials; the words are either written in full or shortened by their chemical symbols. A series of letters and numbers strung together can be hard to remember and even harder to pronounce, and battery chemistries are also identified in abbreviated letters. Such as lithium battery.
For example, lithium cobalt oxide, one of the most common Li-ions, has the chemical symbols LiCoO2 and the abbreviation LCO. For reasons of simplicity, the short form Li-cobalt can also be used for this battery. Cobalt is the main active material that gives this battery character. Other Li-ion chemistries are given similar short-form names, such as Li-ion battery.