"Tartan" is the word used for a checkered pattern, and "plaid" is the word used for a piece of cloth that has a checkered pattern on it. The two terms are nearly interchangeable.
Originally, the terms "tartan" and "plaid" were not interchangeable. However, since plaid fabric generally cannot exist without a tartan pattern, the two terms usually go hand in hand. Therefore, it has now become acceptable to use the terms interchangeably in everyday conversation. Traditionally, tartan patterns are woven into wool cloth, and the criss-crossed stripes that form a rectangular pattern are generally made up of several different colors.