The four options in plain English
LLC (limited liability company). A company you form with your state. It separates business debts from your personal assets, and by default the IRS ignores it for income tax: a one-owner LLC is taxed like a sole proprietorship and a multi-owner LLC like a partnership (IRS: LLCs). You pay income tax plus self-employment tax on the profit.
S-corp (S corporation). A tax status, not an entity. An LLC or corporation files Form 2553 to be taxed under Subchapter S. Profit still passes through to the owners' personal returns, but owners who work in the business are paid a salary through payroll, and only that salary carries Social Security and Medicare tax (IRS: S corporations).
C-corp (C corporation). The standard corporation. It pays its own federal income tax at a flat 21% (Form 1120 instructions), and when it pays out dividends, shareholders pay tax on them again (IRS: forming a corporation, IRS Topic 404, IRS Publication 542).
Partnership. Two or more people running a business together for profit form a general partnership, often without any state filing. Profit passes through: the partnership files Form 1065 and each partner reports a K-1 share on their own return (IRS Publication 541). The catch is liability: general partners are personally on the hook for the business's debts. Two registered variants add a shield: a limited partnership (LP) protects its limited (passive) partners, and a limited liability partnership (LLP), often limited to licensed professions, protects partners from each other's malpractice. A multi-member LLC is taxed as a partnership by default too, but keeps the LLC's liability shield.
Official overviews: U.S. Small Business Administration (SBA): Choose a business structure · IRS: Small Businesses and Self-Employed