The cerebellum and cerebral cortex are distinct parts of the brain with different functions. The cerebellum, located at the back of the brain, coordinates voluntary movement, balance, posture, and motor learning. It also assists with some cognitive functions. The cerebral cortex, which covers the cerebrum, plays a crucial role in higher cognitive functions like perception, consciousness, memory, language, and decision-making. It is involved in sensory processing, motor control, and generating conscious awareness.