Whether it is called wu long or oolong, the name referrers to the same type of tea.
Some folks also know it as "brown tea", and when it was first mentioned in the Chinese literature, it was once called "rock tea". Probably because it is grown in rocky and sandy soils high in the Chinese mountains.
So why are there two different names for this one type of tea?
The reason for the different spellings is because "Oolong" is a Chinese name, and since the Chinese language does not involve the Roman alphabet which consists of letters instead of characters, we get two different pronunciations.
See Wu long tea characters below :
The spelling "Wu-long" is just an English pronunciation translation from the original Mandarin characters. And there are several different ways for Romanizing the Mandarin language. Two common systems are the "Wade Giles" and "Pinyin" translating styles.
The first character in the above picture is pronounced "wu" or "oo", the second "long", and the third "cha". Cha is Chinese for "tea". So combine the three characters and you get either "wu-long-cha" or "oo-long-cha"...which translates in English to: wu-long tea or oo-long tea.
Saying "Wu long" is the Pinyin system, and "Oolong" the Wade Giles style.
So however you are comfortable referring to this type of tea is up to you, it will mean the same.
For me, well, I just enjoy the full flavor and delightful aroma of the brew, and let the tea speak for itself!