A shrimp is a shrimp; a prawn is, well, a shrimp. The two words are used interchangeably in markets and restaurants everywhere. The textbooks may agree that a shrimp is a shrimp, but many people (and quite a few cookbooks) refer to this most popular of shellfish as a prawn.
Some people say the difference is size. In many parts of the country, small and medium shrimp are sold simply as shrimp, while large, extra-large, and jumbo shrimp are called prawns. Unfortunately, this "rule" doesn't always hold. In some areas, all shrimp, small and large, are sold as shrimp, while in other regions, all you'll find are prawns.