As an educator of English language, literature, and linguistics, I can confirm there is no actual difference between the words. "Holistic" is the formal academic spelling of the word, while "wholistic" is an Anglican version of the spelling [as someone mentioned above.] Both spellings are informally recognized, and both have the same effectual meaning.
Confusion often arises because of the increased familiarity with the term "holistic medicine". It's what we call a "non-coined" term. The original word existed before the modern association, but its definition has now become almost exclusively paired with the medicinal practice. In day-to-day use, people tend to automatically slant the meaning of the word towards medicine in their minds.
In the end, the words are interchangeable, though "wholistic" is not academically recognized.