Whether you lift lighter weights or heavier weights until you can't do any more reps, both ways give you the same muscle growth and strength gains if you're already used to training.
Evidence from Studies
Supporting (2)
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Neither load nor systemic hormones determine resistance training-mediated hypertrophy or strength gains in resistance-trained young men
Divergent Strength Gains but Similar Hypertrophy After Low-Load and High-Load Resistance Exercise Training in Trained Individuals: Many Roads Lead to Rome.
Contradicting (3)
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Low-Load Resistance Training to Volitional Failure Induces Muscle Hypertrophy Similar to Volume-Matched, Velocity Fatigue
Effects of Resistance Training Performed to Failure or Not to Failure on Muscle Strength, Hypertrophy, and Power Output: A Systematic Review With Meta-Analysis.
Gold Standard Evidence Needed
According to GRADE and EBM methodology, here is what ideal scientific evidence would look like to definitively prove or disprove this specific claim, ordered from strongest to weakest evidence.