By definition, CR2032 are Lithium Manganese Dioxide (LiMn02) primary cells, which is to say they are not rechargeable.
BR2032 are also primary cells but based on Lithium Carbon Monofluoride so can tolerate a broader range of temperature environments and feature a more constant voltage, but are unsuited for higher current drain. They are also not rechargeable.
LiR2032 are the usual rechageable, Li-Ion versions of coin cells in this size. They are higher voltage at 3.7v nominal (so max charge is 4.2v) but hold only 35-50mAh of energy compared to the ~220mAh the above cells can deliver at low currents. These used to be called RCR2032 but Renata seems to have commandeered that designation for their brand of CR2032 cells.
Maxell has developed a 3.0v nominal rechargeable Manganese Dioxide Lithium cell called the ML2032. It obviously requires a special charger or will explode from overvoltage, and is usually charged in the devices they are intended to power such as the solar charging Logitech K750 wireless keyboard.