Weight lifting is a form of anaerobic exercise. It is very demanding, requiring a great deal of energy, which quickly depletes the body's oxygen reserves. Sprinting and push-ups are other examples of anaerobic activities. They each create a situation called oxygen debt, which requires us to breathe deeply and rapidly in order to restore a proper oxygen level to the muscle cells.
If oxygen reserves become depleted while exercising, muscles convert a starch, called glycogen, into energy. This conversion process creates a waste product called lactic acid.
Jogging is a form of aerobic exercise. Exercising over a long duration requires a steady level of energy for the body. If properly conditioned, the body will be able to supply adequate oxygen to meet its energy requirements during aerobic exercise and much less lactic acid will be formed in the muscles.