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The correct term that describes the balance between the amounts of fat and muscle in the body is body composition. Body composition is a critical concept in health and fitness that provides insight into an individual's physical state by differentiating between fat mass and lean mass (which includes muscle, bones, and water). Understanding body composition is essential for assessing health risks, designing appropriate training programs, and achieving specific fitness goals.

While body weight merely refers to the total mass of a person, it does not provide information on how much of that mass is fat versus muscle. Body mass index (BMI) is a calculation that uses height and weight but does not distinguish between fat and muscle, leading to oversimplified interpretations of health. Body fatigue, on the other hand, refers to a physical state of tiredness and does not relate to the proportion of fat and muscle in the body. Thus, body composition is the most accurate and relevant term for assessing the balance of fat and muscle.