Is Wade-Giles "Shih" pronounced the same as Pinyin "Shi"?
If you are considering the phonemes only and not taking into account tone, then the answer is yes. But if you want to get the most accurate answer about whether or not they correspond to the same sound in Chinese, then you should include a tone. 

Shí and shih2 (the 2 should be superscripted) are both romanizations of the character 石 in the Chinese name 蔣介石.