A for-profit is formed to make a profit for its owners.
A nonprofit is formed for a primary purpose other than making a profit. Usually, this purpose is for the public good.
Both types of corporations are formed at the State level.
How do you decide which one your proposed company will be?
One easy question to consider - who is paying for your product or service?
If you sell products or provide services to people, you are probably a for-profit.
If you make products or provide services to people who can't afford them, and want other people to pay for it, you are probably a non-profit.
Think about bicycles for a moment. All kids would probably love to have a bicycle. It's faster than walking and lets you get around more areas of the neighborhood. (I loved my bicycle as a child.)
Joe's Bicycle Shop
Joe's Bicycle Shop is a for-profit bicycle store will purchase bicycles at wholesale (or build them from raw materials) and then sell them to the public at a higher price that what it cost to make them, producing a profit. After all of the expenses are paid, the owners can keep the rest of the money.
When Joe's Bicycle Shop first opened, the owners will have to pay for all expenses until they start selling bicycles. If they can't afford all the costs, they can look for investors who will expect part of the profits, in the form of dividends.
Business Model: For-profit
Owners: Joe Ciclista
Investors: Frank Ciclista (Joe's brother)
Donors: none, for-profits have investors
Funding: Owners, Investors
Profits: split between investors and owner
Bicycle Cost: $70
Bicycle Retail Price: $120
Nonprofit - Bikes for Kids
Bikes for Kids is a nonprofit bicycle organization that provides bicycles to children in need. Bikes for Kids will purchase bicycles (or ask Joe's Bicycle Shop to donate bicycles) and give them to children who need bicycles. Bikes for Kids decides which children it will serve - by family income, sex, neighborhood or other criteria. They make no money from sales, since the bicycles are given away. With no profits, investors will be hard to find.
So, Bikes for Kids needs other ways to raise funds. The usual ways to raise money for a nonprofit are donations and grants. (Some nonprofits also charge fees based on their services but in this case, the nonprofit has decided to donate the bicycles to the children, so fees don't apply.) After all the expenses are paid, the rest of the money goes towards achieving the mission of the nonprofit.
If a nonprofit is also tax exempt (a 501(c)(3) organization), then donations to it are deductible (within limits) to the donor. This is a reason for people to donate to the organization. (The main reason should be that the donor believes in the mission.)
So, investors get dividends, donors get deductions.
Business model: tax-exempt nonprofit
Clients: children in single-parent homes in the City of Dallas, who receive CHIP
Owners: None, nonprofits are managed by a board of directors
Investors: None, nonprofits have donors
Donors: individuals, Joe's Bicycle Shop (10 bicycles)
Funding: Board, Donations, Grants
Profits: reinvested in the mission
Employees: none, volunteer-based
Bicycle Cost: $70
Bicycle Retail Price: $0, donated to clients
Bikes for Kids incorporates as a Texas nonprofit and then files for its 501(c)(3) designation. After receiving the designation, it begins fund-raising - it puts tip jars at local bicycle shops ("You have a bike, help a kid get one!"), it accepts donations on its website, it has a stand at the local bike trails to explain its mission and it applies for grants to purchase bicycles. It uses its income to purchase bicycles. It then provides bicycles to needy children. The kids get bikes, the donors get tax deductions, the nonprofit gets enough money to continue working.
So, first you do your State filing and become a nonprofit corporation. Then, you file for your 501(c)(3) and are designated as tax exempt. Both of these require that you have a purpose other than making a profit.