The tensing of your muscles is due to them filling with more blood than at rest to ensure that the transmission of oxygen to the cells matches the increase in demand because of your activity.
During power exercises such as sprinting, when the rate of demand for energy is high, glucose is broken down and oxidized to pyruvate, and lactate is then produced from the pyruvate faster than the body can process it, causing lactate concentrations to rise 1. It's is commonly understood that a surplus of lactic acid causes a "burning" feeling in muscles.
Exercising for longer at a lighter weights could b described in this case as akin to running 200m. Your body can't keep up with the increase in lactic acid because of the long duration (and isolation) of the strenuous activity. You feel the burn. If you were sprinting 30m you would not get overloaded with lactic acid and you would not feel the burn.
Endurance training is all about developing your mid and body to deal with this lactic acid build-up.
Side Note: Being sore is not evidence of a good workout