"Large" arteries and "small" penetrating arteries are both involved in stroke
The "large" arteries include both the extracranial portions of the carotid and vertebral arteries, and their large intracranial branches. The intracranial branches lie in the subarachnoid space on the surface of the forebrain and brainstem. These large arteries give rise to "small" arteries, which are the vessels that actually enter brain tissue and ultimately branch to form rich capillary beds where oxygen exchange occurs.

The vast majority of ischemic strokes involve narrowing or blockage of the large arteries.  Hemorrhagic strokes are about equally divided between rupture of large and small arteries.

In small vessel strokes, the small arteries that penetrate into deep central structures of the forebrain and brainstem (like the thalamus or parts of the basal ganglia or medial pons) are most often involved. High blood pressure is the single most important risk factor for stroke, and these small arteries are particularly vulnerable to being damaged by its effects. Perhaps this is because these vessels are already somewhat compromised by their right angle branching and thinner muscular walls, or perhaps they are subjected to higher pressures or more turbulent flow because they have very small diameters. In the extremely elderly, small arteries may also be affected by additional types of pathology.

Strokes affect the forebrain most often, the brainstem or cerebellum less often, and the spinal cord rarely
This presumably reflects differences in the volume of tissue and in the sizes and arrangement of the vessels that supply these regions.