A corporation with a simple capital structure may have only one type of stock, which would normally be common stock. However, a corporation may have a more complex capital structure with multiple types of stock, such as common stock and preferred stock. Indeed, a corporation may have more than one type of common stock or preferred stock. In such cases, the common stock and preferred stock will generally be referred to as separate "classes" of stock. If the corporation has multiple types of preferred stock within the class of preferred stock, those will often be called series of preferred stock.
The question of whether a two types of stock are different classes has important implications in corporate law, securities law, and taxation, among other areas. In corporate law, separate classes of stock are sometimes entitled to vote separately as a class on corporate events (e.g., certain amendments to the certificate of incorporation under DGCL Section 242(b)(2)). In securities law, for example, Section 13(d) reporting is based ownership of "classes" of equity securities. In federal taxation, for example, having multiple classes of stock eliminates eligibility as a S Corporation. Each of these contexts will have different tests for distinguishing different classes of stock.
The concept of classes of stock should be distinguished from series of stock, which are different types of stock within the same class. For example, within the class of a company's preferred stock, there may be Series A Preferred, Series B Preferred, and so forth. The distinctions between classes and series can be somewhat arbitrary, but at a minimum preferred stock will generally be considered a separate class from common stock.