No. In the United States, the everyday word “foundation” is not the same as “nonprofit,” and it is not itself a federal tax classification.
Under IRS rules, every organization that qualifies as tax-exempt under Internal Revenue Code section 501(c)(3) is classified as either a public charity or a private foundation. Private foundations are a kind of 501(c)(3) charitable organization—typically with a narrow funding base—but many entities use “Foundation” in their legal or brand name without being a 501(c)(3) nonprofit at all.
Source: IRS — Private foundations (also see Determine your foundation classification).