There are a few areas of overlap between neurosurgery and neurology, such as stroke care, but for the most part, the fields are very different.
The neurosurgeon handles a lot of spine cases (50%+ even in academic practices). These include spinal stenosis, herniated disc, congenital malformation, traumatic injuries, infections and oncology, plus a few more I'm sure I missed. In regards to spine work, the neurosurgeon may manage the patient medically (ie. with pain meds, steroid injections, physical therapy) or surgically via laminectomies, fusions, foraminotomies.
Neuro-oncology is another big neurosurgical area, basically, this is the scooping out the brain tumor arena. But with the advent of gamma knife (focussed radiation) and genetic identification and treatment (via Cleveland Clinic and UCSF research), one day this field will shrink down as we will no longer have to open up your head to kill the tumor. One cool recent innovation for neurooncology (and other subset of neurosurgery as well, but I've seen this used almost exclusively in oncology cases) is the "stealth MRI". Imagine taking a series of MRIs of a patients head and then uploading it into a million dollar computer that you wheel into the operating room. Then with the patient on the OR table, you take a magnetic wand and touch it to a spot on the patient's head and the computer shows you on the MRI image of the brain where the wand is! The wand is kept sterile so that when you open up the skull and stick the wand into the brain, it'll show you where the tip of the wand is located (very approxiamate since the brain shifted with surgery, but the accuracy is good enough for brain surgery).
Neurovascular is a cool neurosurgery field with two main components: Traditional neurovascular work and endovascular work. Traditional neurovascular surgery is raunchy stuff like clipping aneurysms and extra-cranial/intra-cranial anastamosis for things like carotid stenosis and moya-moya etc. Endovascular work is new to neurosurgery, although interventional radiologist have been doing it for a long time. The main neurosurgical practice of endovascular work involves visualization of cerebral vasculature and usually placement of thrombogenic coils into the lumen of aneurysms to create a thrombus and thus sealing it off from the main vasculature (known as "coiling an aneurysm"). This is a big deal in the SUNY Buffalo program as they are known for this procedure.
Neurotrauma is a favorite area of mine in neurosurgery. It involves mainly two surgical procedures, placement of an extraventricular drain (EVD) and evacuation of blood clot (subdural, epidural etc). These are very junior resident level procedures, taking no more than 45 mins each. The rest of neurotrauma is basically critical care: intracranial pressure management and keeping the brain swelling from herniating the brain. Research is very intense in this field but little result has been fruitful.
Pediatric neurosurgery is another subfield of neurosurgery that I just don't know much about. I think they manage a lot of ventriculo-peritoneal shunts for hydrocephalus kids. They probably also do a lot of meningocoele work too, but I really don't know much about the field.
Functional neurosurgery is the newest area of neurosurgery. It is the deep-brain stimulation (DBS) field, where parkinson patients receive a "brain-pace-maker" to stimulate a ganglion in their basal ganglia to control their parkinsonian symptoms. As you can see, I know very little about this field too.
Neurology is a completely different beast. Firstly, they don't operate.
Secondly, they handle cases like headaches, epilepsy, parkinsons, alzhiemers, uh...hmm...I'm sure they do more than that, but jeez, it's been almost 2 years since I've been on a neurology service! Either case, they use medicine rather than medicine/surgery on their patients. Of course, I feel that neurosurgery is more fun, but I'm very biased.
For more info on neurosurgery and neurosurgery residencies, check out
www.nsmatch.com. It was started by an applicant of the 2004 match and has grown a bit.