A dry cell consists of a zinc anode and powdered manganese dioxide carbon cathode. The electrolyte is a paste of ammonium chloride and zinc chloride.
The Zn anode is oxidised from Zn to Zn2+. The 2 electrons travel through the circuit to the carbon cathode and into ammonium chloride which is reduced to ammonia and hydrogen. Manganese is reduced from the +4 to +3 oxidation state by the hydrogen.
Zn --> Zn2+ + 2 e-
2 NH4+ + 2 e- --> H2 + 2 NH3
2 MnO2 + H2 --> Mn2O3 + H2O
2 NH3 + Zn2+ --> [Zn(NH3)2]2+
Lithium ion batteries consist of a carbon anode and a metal oxide cathode. The elctrolyte is a lithium salt in an organic solvent. Lithium ions are extracted from the anode leaving electrons behind. The electrons travel through the circuit to the metal oxide cathode where lithium ions are inserted. The metal is reduced from Mn+ to M(n-1)+