The term "capital" is used in a wide variety of contexts in corporate law. In almost all cases, capital refers to some portion (or all of) the assets or resources (especially money) that come from sources outside of the corporation to finance the corporation's activities. These sources, of which the most common are investors and creditors invest money in or lend money to the corporation and thereby "capitalize" the corporation.
The narrowest version of "capital" is the legal capital of the corporation. Capital in this sense typically refers to the aggregate amount of par value allocable to capital stock that has been issued by the corporation. This "legal capital" is a special type of resource because it generally must be retained within the corporation (not distributed to shareholders) for the protection of creditors. This definition is probably the least common use of the term "capital" in business and finance, but is important in the corporate law of impairment of capital states.
The broadest definition of capital, and probably the most common use of the term in business and finance, is all of the money that has been invested in or lent to the corporation. In this sense, the corporation's "capital" is all of its debt plus its equity, which is the same as its total assets (possibly minus retained earnings, which are not "invested" in the company). This definition then can be subdivided into equity capital and debt capital. Equity capital is the capital that results from the corporation selling stock to shareholders. Debt capital is the capital that results from the corporation borrowing money from lenders.