Moyamoya disease is a chronic, occlusive cerebrovascular disease with unknown etiology characterized by bilateral steno-occlusive changes at the terminal portion of the internal carotid artery and an abnormal vascular network at the base of the brain. These diagnostic criteria of the moyamoya disease, stated by the Research Committee on Spontaneous Occlusion of the Circle of Willis (moyamoya disease) in Japan, are well established and generally accepted as the definition of this rare entity. On the contrary to the diagnosis of definitive moyamoya disease, there is some confusion in the terminology and understanding of quasi-moyamoya disease; moyamoya disease in association with various disease entities, such as atherosclerosis, autoimmune diseases, Down syndrome, etc. Although the clinical management is not affected by these semantic distinctions, terminological confusion may interfere with the international collaboration of the clinical investigation of these rare conditions. In this article, we sought to review the international standard and regional differences in the diagnosis of moyamoya disease and quasi-moyamoya disease.