The first and most important difference between a for-profit and non-profit business is the profit. It is the distribution of the remainder of the profits that is one of the differentiating characteristics between for profit and non-profit organizations. In a for profit organization the profits that are not re-invested in the organization are distributed to the owners of the corporation as cash. In the case of a non-profit organization the profits are used to provide goods or services to the group or groups the non-profit was formed to help. A religious organization may use the profits to help its members or others obtain food, medical care, education, etc. A university may use its profits to provide free or low cost education to some or all of its students. The point is that the profits of a non-profit organization always go toward supporting some cause that society deems as good and beneficial and not into the pockets of the investors.
The second difference, which explains the first, is ownership of the corporation. A for profit corporation is created when investors get together and transfer assets, money and/or talent to start the corporation. The corporation, which is actually a fictitious person in the eyes of the law, takes title and ownership of the assets, etc. and gives, in exchange for the assets, ownership shares in the company to those who contributed the assets. However, with a non-profit, individuals come together and provide assets, money and/or talent to start the corporation. But, these people who create the corporation do not receive any legal ownership in the corporation and, further, have no guarantee that they will be able to retain control of the corporation once formed. All of the assets are now to be used to advance that cause or provide the service for which the non-profit business was created as determined by the corporation's board of directors.