It is largely assumed that Arnold-Chiari syndrome and Chiari malformations are the same thing and that "Chiari" and "Arnold-Chiari" are just synonyms, but the two conditions are quite different indeed. Not few arguments have arisen among professionals, since confusion in the nomenclature may lead to misundestandings and errors in the patient management, especially from a legally point of view.
The huge importance gained by the rare diseases national systems and the creation in many countries of dedicated welfare programs for rare diseases affected patients primary imply issues of correctness in the diagnosis, which often gives access to expensive aids and treatments. For example, it happens in Italy that Arnold-Chiari syndrome but not Chiari malformation is included as a rare disease in the Ministerial List of Rare Diseases.
The original nomenclature, based on the revision of large amounts of literature and the consultation of the major databases (i.e. OMIM, ICD-10, etc) is in accordance with the following classification:
Chiari Malformation type I (CM1)
Chiari Malformation type II (CM2, a.k.a. Arnold-Chiari syndrome or Arnold-Chiari malformation)
Chiari Malformation type III (CM3)
Chiari Malformation type IV (CM4, not universally recognized)
Let's immediately say that Arnold-Chiari syndrome (a.k.a. CM2) IS a rare disease (i.e. with a prevalence < 1:2.000/2.500), while CM1 IS NOT a rare disease, having an estimated prevalence of 0.1-0.5% with a slight female predominance. It is of consequence that while Arnold-Chiari syndrome patients are entitled to access facilitations in the context of rare diseases systems, CM1 patients do not have the same right. CM1 patients can suffer from even severe symptoms, but Arnold-Chiari syndrome is undoubtely a more serious condition, being unvariably associated with spina bifida.
The partial overlap between the two conditions is surely the cause of their eponyms misuse. Indeed the literature is very clear: Chiari first described the protrusion of the cerebellar tonsils through the foramen magnum (CM1), while Arnold described the variant in which there is the descent of the cerebellar tonsils, cerebellar inferior vermis, and portions of the cerebellar hemispheres into the spinal canal along with displacement of the brainstem and fourth ventricle in association to spina bifida and hydrocephalus. As for CM3 (caudal displacement of the medulla and herniation of part of the cerebellum in an occipital or cervical meningocele) and CM4 (not universally recognized, according to some it is the hypoplasia or aplasia of the cerebellar hemispheres and alterations of the pons with marked dilatation of the fourth ventricle, cisterna magna, and basal cisterns) they're extremely rare.
To greater highlight of the differences, it is of note that while CM2, CM3 and CM4 are considered to be primarily neural in origin resulting from neuroectodermal anomalies, CM1 is considered to result from a mesodermal defect.
References
OMIM (Online Mendielian Inheritance in Man) database, MIM numbers 118420 (at http://www.ncbi.nlm.nih.gov/omim/118420) and 207950 (at http://www.ncbi.nlm.nih.gov/omim/207950
Peyman Pakzaban. Chiari Malformation (updated 17 Jun 2010) at http://emedicine.medscape.com/article/1483583-overview
Stevenson KL. Chiari Type II malformation: past, present, and future. Neurosurg Focus. 2004 Feb 15;16(2):E5. PMID: 15209488
Speer CM, Enterline DS, Lorraine Mehltretter, Hammock P, Joseph J, Dickerson M, Ellenbogen RG, Milhorat TH, Hauser MA, George TM. Chiari type I malformation with or without syringomyelia: prevalence and genetics. Journal of Genetic Couseling. 2003, 12(4), 297-311.
McLendon RE, Crain BJ, Oakes WJ, Burger PC. Cerebral polygyria in the Chiari Type II (Arnold-Chiari) malformation. Clin Neuropathol. 1985 Sep-Oct;4(5):200-5. PMID: 4064385.
Peyman Pakzaban. Chiari Malformation (updated 17 Jun 2010) at http://emedicine.medscape.com/article/1483583-overview
Stevenson KL. Chiari Type II malformation: past, present, and future. Neurosurg Focus. 2004 Feb 15;16(2):E5. PMID: 15209488
Speer CM, Enterline DS, Lorraine Mehltretter, Hammock P, Joseph J, Dickerson M, Ellenbogen RG, Milhorat TH, Hauser MA, George TM. Chiari type I malformation with or without syringomyelia: prevalence and genetics. Journal of Genetic Couseling. 2003, 12(4), 297-311.
McLendon RE, Crain BJ, Oakes WJ, Burger PC. Cerebral polygyria in the Chiari Type II (Arnold-Chiari) malformation. Clin Neuropathol. 1985 Sep-Oct;4(5):200-5. PMID: 4064385.