Mild to moderate muscle soreness (DOMS) is normal training response, not injury. Training the sore body part with reduced intensity actually reduces soreness faster than complete rest. Skipping for soreness perpetuates the pattern.
When to push through
Soreness from recent training. No sharp or shooting pain. Full range of motion still available. Reduced intensity (60-70% of usual weight) is fine.
When to actually rest
Sharp pain. Joint discomfort (not muscle). Severe restriction in range of motion. Sustained pain over multiple days without improvement.