These most commonly refer to what is known as Dysarthria and Apraxia of Speech.  Dysarthria refers to poor control and weakness within speech musculature while apraxia refers to impaired sequencing of movements involved in speech production.

A large number of neurological conditions can cause these conditions, in my experience as a speech therapist the most common conditions are Parkinson’s disease, Stroke, Multiple Sclerosis, Amytrophic Lateral Sclerosis (ALS) etc. Dealing with a condition like a stroke or other neurogenic condition is difficult as is, but the effects are exacerbated with the frustration of unintelligible speech, slurred nature of speech, difficulty saying the right sounds, altered speech or voice quality etc.