Form 8832 is used by a Limited Liability Company to choose to be classified for tax purposes (and to be taxed) as other than the default classification. For example, if no election is made a single member LLC is disregarded and a multimember LLC is treated as a partnership. In either of those cases if the LLC wants to elect to be taxed as a corporation the Form 8832 is used.
Form 8832 can also be used to change a prior election.
Form 2553 is used by a corporation to elect to be treated as a pass-through entity (Subchapter S corporation) and to indicate the tax year elected. Similar to partners in a partnership, income of an S corporation generally is taxed to the shareholders of the corporation rather than to the corporation itself.
See LLCs Classified as Corporations
"LLCs electing classification as an S corporation are not required to file Form 8832 to elect classification as a corporation before filing Form 2553. By filing Form 2553, an LLC is deemed to have elected classification as a corporation in addition to the S corporation classification. "
Please ask if you need clarification.