You've got some right (or partly right) and some wrong answers.
You suggested the answer to your own question when you said you are "wondering if the main purpose of the school is to make money." That is right.
- The primary purpose of a for-profit organization is to make money for its owners (*not* the managers ... the owners!).
- The primary purpose of a non-profit organization is something *other* than to make money for its owners.
While the directors (or members of the relevant governing body) of either type of organization may have some other purposes in mind when making decisions, they have a fiduciary duty to pursue the primary purpose, and can be held liable for failing to do so.
The overwhelming majority of schools*, at least in the US, are non-profit organizations. Their primary purpose is to provide an education to students (and, at least in the case of universities, to do research and advance society's knowledge generally). They do *not* have the purpose of making money - indeed, they don't have any owners to give it to if they do.
The charter school you asked about -- like some other charter schools -- is different in this respect from the vast majority of other schools, at least in this country.
Note: non-profit organization frequently do "make money." Of course, they take in money (from, say, tuition), in order to spend it to accomplish their purpose. It is not at all unusual for a school to make profits some years, in order -- for example -- to gather up a fund to build a new building. Some non-profit organizations also have endowments -- money they hold on to and invest, applying the investment proceeds to their purpose -- though these typically are funded by contributions, rather than profits from operations. Also, non-profit organizations may run side businesses solely to make a profit, so that they can use that money for the organization's purpose.
As mentioned, the two types of organization are also taxed differently. As a matter of US federal income taxes:
- a for-profit organization either pays taxes on its income, or its owners pay taxes on its income (e.g. in the case of partnership or S corporation);
- a non-profit organization, if it fits into certain categories in the tax code, generally doesn't pay tax on its income, but may be required to pay tax on its "non-exempt function income;"
- contributions to a non-profit organization whose purpose is considered charitable under the tax code (such as most schools) are deductible to the contributors.
*By "school," I mean ordinary primary and secondary schools and colleges ... not, say, ski schools, driving schools and those sorts of things.