There are 3 main categories of vasculitis. In all types, the blood vessels get inflammed and the organ supplied by that blood vessel can get necrosed (so you can even have a tongue necrosis in something like Temporal arteritis if the blood vessels supplying the tongue are blocked). Symptoms are based on the endorgans affected. Diagnosis usually requires measuring lvls of ESR, certain antibodies (p-ANCA, c-ANCA), and most importantly, a biopsy of the effected tissue.
Large Vessel includes temporal arteritis and Takayasu's. Temporal arteritis (aka Giant Cell arteritis) is common in older females, is associated with polymalgia rheumatica, and involves most commonly the temporal artery. A biopsy is 90% sensitive and there is typically elevated ESR. Takayasu's is found in young Asian women, involves aortic arch and its branches, and is diagnosed with an arteriogram.
Medium Vessel includes Kawasaki's, Churg-Straus, Wegner's gruanulomatosis, Polyarteritis nodosa, and Microscopic Polyangiitis. Kawasaki's is common in kids. Churg-strauss involves many organ systems, p-ANCA association, has poor prognosis, and a biopsy of lung or skin tissue is used to confirm diagnosis. Wegner's granulomatosis usually involves mainly the kidneys and upper / lower respiratory tracts, nodules / infiltrates are found on chest radiographs, there is a c-ANCA association, a very high ESR. Open lung biopsy is performed to confirm diagnosis. Polyarteritis nodosa or PAN has no pulmonary involvement, involves GI and nervosus system vessels, and a biopsy of involved tissue or mssenteric angiography is used for diagnosis.
Small Vessel include Henoch-schonlein purpura, hypersensitivity vasculitis, Bechet's syndrome, and Buerger's disease. Hypersensitivity vaculitis is caused by a drug reaction, infection or other stimuli. There is usually skin involvement: palpable pupura, macules, or vesicles. You have to do a biopsy to diagnose. Bechet's syndrome usually involves oral and genital ulcers and a biopsy is performed for diagnosis.
Buerger's disease (aka Thromboangiitis Oblitans) is associated with smoking and affects arms and legs.