Should you lift heavy, or should you lift lighter to feel the burn?
The quick answer is likely both. Lifting heavier loads in the 8 to 12 rep range with good form causes damage to the muscle that stimulates strength and size progression through muscle disruption.
Lifting lighter weights to feel the “burn” causes an influx of metabolites into the muscle. One of the products of this influx is the commonly known build-up of lactic acid and hydrogen ions. Metabolites, like lactic acid, cause your muscle cells to swell, and degrade, which triggers the repair, or muscle building progress.
How you can apply this
Consider using both heavy, 8 to 12 repetitions, weightlifting and light, 12-20 slow rep, training in your program to get the best of both training modalities. When using 8 to 12 reps, consider stopping a few reps short of failure to manage fatigue. However, when doing 12-20 reps, consider going to failure or, at the very least, getting very close to failure to be efficient. Fatigue management deserves its own chapter but, for now, use those tips to get the broad strokes of the concept.
Science Applied
Mechanical tension is the tension to a muscle produced both by the generation of force, and the stretch of a muscle under load. Mechanical tension is heavily associated with muscle growth and strength progression; this is due to skeletal muscle disruption and degradation. This disruption through tension causes responses from the myofibers of a cell as well as satellite cells.
Metabolic stress, which is the influx of things like lactate, hydrogen ions, creatine, and others either directly or indirectly, is associated with muscle growth via cellular swelling, and muscle fiber degradation, through the creation of a more acidic environment. Cellular swelling stimulates protein synthesis, likely due to the degradation of the intense expansion causes.
One of the main differences in these two training modalities is how heavily they rely on various energy systems. While energy systems are not an on-off switch, one is generally used more heavily than the other. In heavier training, the adenosine triphosphate phosphocreatine system takes on most of the energy responsibilities. On the other hand, lightweight metabolite training involves more of the anaerobic glycolysis system, which causes lactic acid accumulation and the creation of an acidic cellular environment, which is likely why your muscles end up producing less and less force, but that is a topic for another time.
Research shows that a mixture of these methods is most effective at producing maximal hypertrophy over a training macrocycle. Overloading the tissue through mechanical tension, as well as metabolites in a mesocycle, allows optimal progression through all possible avenues.
References
Schoenfeld, B. (2010). The mechanisms of muscle hypertrophy and their application to resistance training. Journal of Strength and Conditioning Research, 24(10).