The IRS, not the state, classifies corporations according to how they want to be taxed. There are two types of corporations according to the IRS, either "C" corporations, named after Subchapter C of the tax code, or "S" corporations, named after Subchapter S of the tax code. C corporations have their own tax identification number and pay their own taxes.
S corporations, sometimes called small business corporations, are taxed as if they were not a corporation. Taxed like a partnership, an S corporation passes through its income or losses to the shareholder's personal tax return and is not liable for Federal income taxes itself. The shareholders of an S corporation pay personal income taxes based on the income of the S corporation, whether or not the shareholder received any of the income. S corporation shareholders can take any losses the corporation may have.
For information about how to handle taxation, see your CPA.