Abstract Logos are logos where the product or service of that company is being represented through an abstract/artistic symbol or icon.
Letterform Logos are logos that use the shape of a letter used in typography, calligraphy, paleography, and epigraphy to represent their company. This can also include numbers and punctuation.
Pictorial Logos, also sometimes referred to as brand marks or a logo symbol, are icon—or graphic-based designs. This type of logo is probably the image that comes to mind when most people think “logo”.
Wordmark Logos are the written name of the organization, company or product, stylized in a way that is meant to stand out in their customer’s mind.