Zip and postal codes serves the same purpose. It is an alphanumeric code assigned to every address or location in a Country, most typically to help the post office deliver the mail.
The difference between zip and postal code is that Unites States of America (USA) uses the term "zip code" while the United Kingdom (UK), Nigeria and some other countries use postcode or postal code.
ZIP is an acronym for Zone Improvement Plan. In earlier days the Post Office broke up large cities into geographic zones for faster sorting. In 1963 the Post Office introduced the ZIP Code system to replace the zone system. Several years later the US Postal Service expanded the system by adding more digits, ZIP + 4.
Nigeria uses a six digit postcode assigned to streets and locations across the country by Nigerian Postal Service (NIPOST).