Desdemona,
Yes, I was first diagnosed with vasculitis and then later moyamoya.
Vasculitis is the inflammation of blood vessels in your brain. Vasculitis can be in any organ of your body (heart, lungs, etc.), but is more rare in the brain. IMO, I'm not sure that with vasculitis you would have the moyamoya vessels (the vessels that appear as the "puff of smoke" on your MRI/MRA or angiogram scans). This is what is a sure sign of moyamoya.
The other big differentiation from what I've read is that vasculitis is more difficult to diagnose with a MRI/MRA and/or angiogram; whereas, with either of these tests in a moyamoya patient, it is easier to decipher that you have moyamoya disease because of the moyamoya vessels, i.e., "puff of smoke". The only true test that someone has vasculitis is through a biopsy of the brain tissue and examing it under a microscope. This test is used as a last resort.
The similarity between MM and vasculitis are in the symptoms. They can be headaches, behavioral disturbances, confusion, seizures, strokes, and TIA's....among others.
Treatment of vasculitis differs from moyamoya. With MM, the only treatment for the disease is through surgery (the kind depending on what a specialist feels is the best one for your case). In vasculitis many cases do not require treatment depending on the severity. Most physicians recommend cortisone-type medications (steroids), such as Prednisone, Prednisolone, or methylprednisolone (Medrol) as the initial treatment for vasculitis. Some people with severe vasculitis or vasculitis that does not respond well to cortisone-type drugs will need to be treated with cytotoxic drugs. These medications kill the cells that cause inflammation in the blood vessels. The two most frequently used are azathioprine(Imuran) and cyclophosphamide (Cytoxan). They are usually used in combination with Prednisone and are often effective in treating vasculitis.
In answer to your question regarding whether you can have moyamoya on only one side of the brain....the answer is yes.
I hope this has helped in some way. If you have any other questions, please don't hesitate to ask.

Michelle