ZIP or Zone Improvement Plan Codes were created by the U.S. Postal Service to improve mail delivery service. They are based on postal routes which factor in delivery-area, mail volume, and geographic location. They are not designed to hold population data and change frequently. Some ZIP Codes may only include P.O. boxes or cover large unpopulated areas.
ZCTAs or ZIP Code Tabulation Areas were created by the U.S. Census Bureau and are generalized representations of ZIP Codes that have been assigned to census blocks. Therefore, ZCTAs are representative of geographic locations of populated areas. In most cases, the ZCTA will be the same as its ZIP Code. ZCTAs will not necessarily exist for ZIP Code areas with only businesses, for single or very few addresses, or for large unpopulated areas. Because ZCTAs are based on the most recent Census, they are more stable than ZIP Codes and do not change as frequently.
For more information please see the Census Bureau's ZCTA reference page.