The molecule necessary for respiration to occur in both plants and animals is NADH. There are two types of respiration, aerobic and anaerobic respiration. Aerobic respiration requires oxygen for it to work while anaerobic respiration does not need oxygen.
In both aerobic and anaerobic respiration, the NADH molecule is part of the enzyme complex and must be restored to its NAD oxidized state. If oxygen is available, the NADH molecule is transported to the mitochondria where it can be converted back to NAD and plays a role in the electron transport chain
In oxygen deficient conditions, NADH gets converted back to NAD through anaerobic mechanisms.
So this molecule NADH is crucial for both aerobic and anaerobic respiration.