difference between a neurologist and a neurosurgeon?

Seriously?
You can as well add cardiologist and cardio surgeon

Neurologists

Neurologists specialize in the diagnosis and treatment of diseases or conditions occurring in the brain and nervous system, as well as their supporting systems and tissues. Some focus on neurophysiology, using diagnostic tests such as electroencephalograms and electromyography to detect neurological conditions. Others specialize in the treatment of neurodevelopmental disorders, attempting to manage cerebral palsy, learning disabilities and similar chronic conditions. Neurologists might also specialize in pain management, treating patients with debilitating chronic pain or acute short-term pain. Vascular neurologists study and treat conditions of the circulatory system that affect the function of the brain or nerves.


Neurosurgeons

Neurosurgeons use a variety of therapies, from endoscopic microsurgery to radiation to traditional open surgery, to treat neurological conditions. These include traumas of the brain and spine, tumors, strokes and aneurysms, and many other conditions of the spine, brain and skull base areas. These are complex areas of practice, and neurosurgeons' work often overlaps with that of neurologists, orthopedic surgeons, and plastic or reconstructive surgeons. Often, several of these practitioners will work collaboratively with a single patient to ensure a successful outcome in complex procedures.

Similarities and Differences

Neurosurgery is closely aligned with neurology, and both require an in-depth understanding of the nervous system and its functions. Conditions that require management, or can be improved by medications or other therapies, are generally treated by neurologists. Neurologists are also more likely to act as diagnosticians, isolating and defining neurological conditions for neurosurgeons to rectify. When diagnosis reveals a physical cause for neurological conditions, neurosurgeons can usually perform a surgical procedure to remove or correct that condition, often bringing about a dramatic improvement in the patient's condition. Both neurologists and neurosurgeons can use minimally invasive endoscopic or catheter-based procedures, using miniature instruments to repair or reinforce blood vessels in the brain.


Income

One key difference between neurology and neurological surgery is income. Neurosurgeons out-earn their neurologist peers by a substantial margin, beginning in their first year of practice. Medical recruiting firm Profiles, which specializes in new physicians, reports a median first-year income of $190,000 for neurologists, while neurosurgeons starting practice earned a median income of $395,000 a year. Across all career stages, the American Medical Group Association reported a median income of $236,500 for neurologists and $592,811 per year for neurosurgeons. Staffing firm Jackson and Coker found an even broader disparity, reporting an average salary of $209,394 for neurologists but $671,086 per year for neurological surgeons.

http://work.chron.com/difference-between-neurosurgeon-neurologist-6843.html

feedthenation:
Medical recruiting firm Profiles, which specializes in new physicians, reports a median first-year income of $190,000 for neurologists, while neurosurgeons starting practice earned a median income of $395,000 a year. Across all career stages, the American Medical Group Association reported a median income of $236,500 for neurologists and $592,811 per year for neurosurgeons. Staffing firm Jackson and Coker found an even broader disparity, reporting an average salary of $209,394 for neurologists but $671,086 per year for neurological surgeons.

http://work.chron.com/difference-between-neurosurgeon-neurologist-6843.html

Why be-labour yourself over a simple harmless question. The OP isn't your examiner, neither is the question a Part II essay question.
@OP, the difference is that a neurologists is the physician who specializes in the function or otherwise of the brain and nervous system while the neurosurgeon is the specialist in surgeries involving the brain and nervous system.

Common neurological disorders that a neurologist may treat include headaches, sleep disorders, tremors, epilepsy, brain, and spinal cord injuries, brain tumors, strokes, Alzheimer's disease, Parkinson's disease, multiple sclerosis (MS), amyotrophic lateral sclerosis (ALS), and peripheral nerve disorders. Neurosurgeons are trained to treat people with trauma to the brain and spine, aneurysms, blocked arteries, chronic low-back pain, birth defects, tumors in the brain and spinal cord, and peripheral nerve issues.

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