Arnold Chiari:
A congenital anomaly resulting from a normal-sized cerebellum developing in an abnormally small posterior fossa with a low tentorial attachment. There is a narrow craniospinal junction and malformation of the posterior fossa leading to downward displacement of the medulla, fourth ventricle, and cerebellum into the cervical spinal canal, as well as elongation of the pons and fourth ventricle. This results in impaction of the foramen magnum, compression of the cervicomedullary junction by the ectopic tonsils, and interruption of normal flow of cerebrospinal fluid (CSF). Two types, type I is asymptomatic (till adulthood) and type II is symptomatic and commonly associated with syringomyelia and meningomyelocele respectively. Symptoms arise from dysfunction of brainstem and lower cranial nerves.
Dandy Walker:
Also congenital but this time there is agenesis or hypoplasia of the cerebellar vermis, cystic dilatation of the fourth ventricle, and enlargement of the posterior fossa with aqueductal obstruction leading to hydrocephalus or it may be associated with atresia of the foramen of Magendie and foramen of Luschka.
The enlarged fourth ventricle balloons out backward as a membrane-wrapped cyst and lifts and displaces the posterior portion of the brain, as well as cause an internal obstruction of normal CSF flow, with resultant supratentorial hydrocephalus.
Unlike Arnold Chiari, the posterior fossa is large ( there's a lot of space in the post fossa for the 4th ventricle to WALK around and expand).