COMPARE this province:
陕西 [shǎnxī] ->西安 [xī'ān] - Shaanxi province (capital: Xi'An)
WITH the similarly-named province:
山西 [shānxī] -> 太原 (tai4yuan2) - Shanxi Province (capital: Taiyuan)
Note that the pinyin is the same, 'shanxi', therefore the spelling is different in English, with an added a for the province further West. Why? I like to think the 3rd tone creates a longer 'ah' sound, almost sounding like two syllables to a native English speaker.