It certainly can be confusing. I generally use the term "nonprofit" to mean a corporate entity formed under a nonprofit corporation act, e.g., one derived from the Model Nonprofit Corporation Act. This says nothing about the tax status of the entity, and unless other circumstances also apply the entity would be subject to taxes in the same way as a for profit company on its net income. But many nonprofits also take steps to qualify for one of several tax exemptions, the most well known being section 501(c)(3). Not all of the familiar tax advantages apply to all tax exempt organizations. For example, donations to an organization exempt under 501(c)(3) are deductible by the donor, but donations to a 501(c)(4) are not.