What is the difference between nonprofit and tax-exempt?

There is a big difference between “non profit” and “tax exempt.”
Nonprofit status refers to status under state law.
Tax-exempt status refers to federal income tax exemption under the Internal Revenue Code.
501(c)(7) Social Clubs: Tax-Exempt Country Clubs, Fraternities & Golf Clubs

What is a 501(c)(7) organization?
Not all tax-exempt organizations are private foundations or public charities. Under 501(c)(7), social clubs like fraternities or country clubs can be recognized as tax-exempt organizations.