What is the difference between a non-for-profit and for profit? And can both do fundraiser?

To begin I assume you are speaking of the two different types of corporations authorized by the state statutes - the for profit corporation, and the non-profit corporation.

For profit corporations are entities formed by individuals (called shareholders). Their purpose is to engage in business. The goal of the for profit corporation is to make money that can be distributed to the shareholders, either in the form of owner distributions, dividends, or as a result of a sale of the business.

Non-profit corporations are also formed by individuals (often called members), but their purpose is not so much to engage in business (although, within certain limits, they can), but instead to accomplish a purpose. There are many kinds of non-profit corporations. Some are for charitable purposes, and pursue religious, educational, scientific or other goals. Some are trade or business organizations (like a chamber of commerce or a trade association). Some are social clubs. The common theme among non-profits is they are not organized to make money for distribution to their members. Although they can pay salaries to employees, they cannot distribute their net income to their members. They must hold the net income for the purpose of the corporation, whatever that is.

For profit corporations generally do not hold fund raising events. All non-profits may hold fund raisers, but only a charity, which has received a letter from the Internal Revenue Service recognizing its charitable status, can offer its donors an income tax charitable deduction for donations.