I have experience working with nonprofit organizations for ten years and have applied for and received 501(c)(c) status for a charitable organization in the US. Achieving tax-exempt status in the US, for example, requires a very specific process and requires a great deal of scrutiny by the IRS. In the US, one way to achieve tax exempt status is to be a nonprofit 501(c)(3) organization but this only applies to organizations with a charitable purposes. (There are similar designations for churches, associations, and foundations, for example.)
Even 501(c)(3) charities are required to pay sales tax when items are bought and sold by the organization; employees are also required to pay income tax. In the case of 501(c)(3) organizations, tax-exempt status gives the organization an opportunity to receive donations and provide receipts for the value of donations so donors may deduct the donations from their individual taxes; similarly, 501(c)(3) organizations do not pay taxes on donations received.
This is just one example based on my experience in the nonprofit sector in the US. There may be other applicable examples. Best wishes!