Find anyone who works for a large nonprofit, and they’ll likely be familiar with that organization’s IRS acceptance letter (approving the organization’s tax-exempt status).
However, tiny nonprofits often don’t know they’re entitled to the same tax-exempt status without any approval.
According to 26 C.F.R. §508(c)(1)(b), any organization that  qualifies as a nonprofit per 26 C.F.R. §501(c)(3),  is not a private foundation, and  whose gross receipts don’t exceed $5k per taxable year, need not federally apply for tax-exempt status.
This seemingly-minor exemption makes it an order of magnitude easier to save money on supplies for volunteer organizations and the like, as well as to accept small donations from individuals looking to write-off their contribution.
As always, though, consult an accountant and/or attorney for legal and tax advice before proceeding.