The difference between "wellbeing" and "well-being" is simply a matter of spelling preference based on geographical location.
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Well-being (with a hyphen) is the preferred spelling in the United States and Canada.
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Wellbeing (without a hyphen) is the standard spelling in the United Kingdom, Australia, and other English-speaking countries outside of North America.
In essence, both terms refer to the same concept: the state of being comfortable, healthy, or happy. The choice of spelling is purely stylistic.
