Ataxia is a degenerative nerve disorder that causes slurred speech and general lack of coordination.
Aphasia is a language disorder. There are multiple varieties of aphasia, some of which prevent comprehension, and some of which prevent generation. This mute girl seems to be suffering from a form that affects only ability to speak, but does so very pronouncèdly. On the other hand, she might not have aphasia as such, but instead some damage to neuro-muscular system.