BMS is battery management system, always for big battery packs, typical use is LiFePO4 power battery.It has protective functions of over charging,over discharging,over current,short-circuit, cells balancing functions,some battery may need also communication port and data input output options and other display functions. its up to applications requirements.
PCB or PCM is protection circuit board, usually for small battery, typical use is for digital batteries, like mobile phone battery,camera battery,mp3 player battery,GPS batteries,heated clothing batteries and so on. Most time, Its for 3.7V or 7.4V battery, It has four basic functions of over charging, over discharging, short circuit,over current.some batteries may also need PTC and NTC.
Anode of rechargeable lithium battery mostly is made of Lithium ion material, the Li electron goes to both anode and cathode sides once and once again during charging and discharging process,this how it works.In case of over charging,(lithium ion battery can not allow the cell voltage to be higher than 4.25v) the anode tiny hole structure may collapse, hard crystals substances may grow up and cause short circuit, then the temperature will rise up quickly, at last it will lead to a fire.So, over charging protection is needed.
As for short circuit and over current, it’s easy to understand, because in these cases, the internal temperature will be higher and higher, and catch a fire in the battery.
About over discharging, it’s also needs to be avoided, because lithium ion battery can lose large ratio of capacity forever once it was discharged to be too low level, for lithium ion battery cell, the voltage must be higher than 2.7V, if the voltage gets lower than this, eternal damage will happen to the battery.
So at least PCB/PCM must be used for lithium ion battery with basic protections, however for bigger lithium battery packs, it involves lots of battery cells, the unbalance of cells will also cause problems, such as shorter cycle life, low voltage, so on base of above mentioned four protections, balance function is added to make a basic BMS.
(Source from https://www.pdbattery.com/)