Because of the one-class-of-stock restriction, an S corporation cannot allocate losses or income to specific shareholders. Allocation of income and loss is governed by stock ownership, unlike partnerships or LLCs taxed as partnerships where the allocation can be set in the partnership agreement or operating agreement.
LLC taxed as an S corporation First, an LLC would need to elect to be taxed as a corporation by filing Form 8832, Entity Classification Election. After that, an LLC can then file a Form 2553, Election by a Small Business Corporation, to elect tax treatment as an S corporation.
An S Corp is a tax status (totally separate deal). You can elect to be taxed as an S Corp either as an LLC or as a Corporation. If you're self-employed I recommend the LLC; the corporation only makes sense if you're going to be hiring a ton of folks, taking on investors, etc.