501(c)(3) organizations are charitable entities (i.e. trusts, corporations, etc) that are exempt from paying federal income tax. 501(c)(3) is the most common type of nonprofit and/or charitable organization in the US. Common examples are churches, universities, and charitable foundations. 501(c)(3) organizations are intended to be charitable organizations, no individuals or private shareholders may benefit from them.
501(c)(4) organizations are also tax-exempt organizations, but they are not required to be charitable. 501(c)(4) organizations are typically civic leagues, social welfare organizations, and local associations of employees. Unlike 501(c)(3) organizations, 501(c)(4) organizations may engage in political activities and lobbying, and may also accept corporate donations.