"Oolong tea", "wulong tea","Wu-long" are a combination of both phonetic ("sounds like") and dielectic translations of the same class of Chinese tea (Black Dragon Tea in Mandarin).
The different spellings originate because the Chinese (Mandarin) language when written uses symbols to represent syllables, rather than being built up from an alphabet like English.
The process of transcribing spoken Chinese to the western alphabet is known as "Romanising". Several different systems exist. The Taiwanese dialect uses a different system from Mandarin for translating sounds (or "Romanising") to English.
To complicate things further, the province in mainland China famous for Oolong tea is Fujian - which being opposite Taiwan, uses this dialect natively - translating their tea to Oolong, whereas the mandarin system would more readily translate the sound to Wulong. The US English literature seems to have more readily adopted the Wulong variations than some other English speaking countries.