A 501(c)(3) can be a private foundation funded by one donor that gives grants, or a public charity that raises money from the public and runs its own programs. Donations are tax-deductible, but the IRS won't let you start a nonprofit just to save taxes.
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There are a variety of different nonprofits. Sometimes you hear the term 501. I can have a 501 that's a private foundation. This is often going to be where, as the person who sets it up, I'm the only donor into the foundation, and then my private foundation likely donates to other charitable organizations. It's not an operating nonprofit. Or you can have a public charity. Also a 501. This is where you're soliciting funds to find additional donors other than yourselves. You're probably operating the business, so it's more involved. Money that you contribute to your 501 for your purpose is a tax deduction on your personal tax return. You do get a tax savings, but the IRS is very clear. You can't set up a nonprofit for the sole purpose of saving taxes. It's really just a way for you to use pre-tax money on something that you believe in.