see Awake craniotomy.
Awake surgery is broader and can refer to any procedure performed while the patient is awake (even outside the brain).
Awake craniotomy specifically refers to brain surgery performed while the patient is awake, allowing intraoperative cortical and subcortical mapping — crucial for tumors near eloquent areas.
It is the standard term used in:
Scientific literature (e.g., Journal of Neurosurgery, Neurosurgery, Brain)
Surgical textbooks
Clinical protocols in neuro-oncology and epilepsy surgery.