Forebrain
The brain, or cerebrum, consists of all structures in above excluding the spinal cord. The spinal cord is included when considering the central nervous system (CNS). The brain and spinal cord develop from the formation of the neural tube, the brain arising from the anterior (rostral) and the spinal cord arising from the posterior (caudal) portion. Neural development in vertebrates is a process of continual differentiation of structures guided by genetic expression and cellular specialization.
The brainstem consists of the medulla, pons, and midbrain and provides regulatory functions often taken for granted by humans: blood pressure and breathing control (medulla); balance, taste, hearing, face and neck muscle control (medulla, cranial nerves); breathing, sleep, taste, movement coordination (pontine nuclei). These functions, among others, are considered autonomic and often engage rapid sensory-motor integration for things like automatic eye movements. for example
The reticular formation is another important structure of the brainstem, encompassing several nuclei that promote alert states and wakefulness (often called arousal).
Describing what a nucleus is in neural terms