It will depend upon your state's laws whether you must your tags (registration) renewed on that date or if there is a grace period till the end of your month of renewal.
For example in Florida registrations issued in the name of an individual expire at midnight on the day of their birth date, except for mobile homes and commercial vehicles. Mobile homes expire at midnight on the last day of the month of December. Commercial vehicles expire at midnight on the last day of the month of May (if registered semiannually) or December (for annual registration).
If you are stopped and are found that your registration has already expired on the 18th then likely the police could cite you for expired tags. It might be a fix it ticket meaning that you could get it dismissed if you get the car's registration renewed before your court date, this again depends upon state laws and even local law enforcement laws.
In FL if you do pay your registration fees late there are late fees. Section 320.07(4)(a), Florida Statutes, specifically requires the delinquent fee to be imposed on any applicant who fails to renew a registration before the end of the month in which renewal registration is due.
The delinquent fee is applied beginning on the 11th calendar day of the month succeeding the renewal period. The exact expiration date is shown on the current registration certificate; therefore, the registered owner should be well aware of when their registration expires in Florida.
To find out about your state's laws regarding the expiration date of your license plates / registration, you can contact your local Department of Motor Vehicles.