Credit monitoring involves monitoring your credit history for suspicious activity. The three credit bureaus as well as many third parties offer credit monitoring for a modest fee, providing services such as allowing you to check your credit reports every day for theft, receiving e-mail alerts of suspicious account activity, and receiving unlimited scores and credit reports.
Fraud monitoring allows you to monitor public record data bases for suspicious activity. Public record databases can show if someone has broken the law using your identity.
Beware of companies that guarantee they can prevent identity theft. While you can mitigate your risk of becoming a victim and the damage after a compromise, no one can give you a 100% guarantee that you can escape. Even if you do everything right, you might still be on the wrong database at the wrong moment -- during a data breach, for example. Unfortunately, the bad guys are good at what they do and are often one step ahead of the good guys.