This question is a bit tricky to answer. The first critical distinction is between parkinsonism and Parkinson’s Disease. Parkinsonism describes the cluster of symptoms that we associate with Parkinson’s, especially the motor symptoms such as tremor and muscle rigidity, regardless of the cause of these symptoms. Some diseases other than Parkinson’s can present with parkinsonism, usually accompanied by other symptoms not usually associated with Parkinson’s. Certain drugs can also cause parkinsonism in some patients, and if you are lucky, these might even go away when you stop taking the drug; as such, drug-induced parkinsonism can be rather different than Parkinson’s Disease in that it does not necessarily involve degeneration of the dopamine-producing neurons in your brain.
A diagnosis of Parkinson’s Disease (sometimes referred to as primary or idiopathic Parkinson’s) is thus by process of elimination. If other possible causes of your parkinsonism are ruled out or unlikely, then you probably have Parkinson’s Disease. As discussed elsewhere on this site, a small fraction of patients have mutations that we know lead to Parkinson’s disease. These can vary a bit in terms of the age of onset and how quickly the disease progresses, for example, and there can be some differences in the appearance of the brain upon autopsy. There are also some differences, on average, observed in young-onset Parkinson’s patients vs. older-onset. But overall, most clinicians seem to feel comfortable with considering Parkinson’s to be one disease, because the primary underlying cause of the symptoms — degeneration of dopamine-producing neurons — is the same.
At the other extreme, I have heard/seen a number of variations on this quote, primarily from patients: “If you have met one person with Parkinson’s Disease, then you have met one person with Parkinson’s Disease”. The implication being that the symptoms and the experience of having Parkinson’s can vary dramatically from patient to patient. It’s hard to argue against this; no two individuals are alike, and there is indeed a range of symptoms associated with the disease. But I am not sure that Parkinson’s is unusually heterogeneous relative to other diseases, and I personally have been struck by how similar my progression of symptoms has been to that reported by other patients.
That being said, it is generally accepted that meaningful sub-types of the disease can be defined; the most common ‘classification’, which is supported by patient data, is between ‘tremor dominant’ and, well, non-tremor dominant, sometimes referred to by the unfortunate acronym PIGD (postural instability and gait disability). Tremor-dominant is generally associated with slower progression. But as you might guess, the distinction between the subtypes is not super clean; it might be better thought of as a continuum. As far as I can tell, the underlying physiological basis of the different types of symptoms is not terribly well understood, but may have to do with exactly which neurons/brain regions degenerate first.