What is the difference between postal and Zip codes?

They are both multicharacter codes for sorting and delivering mail.

"Postal code" is the generic term for such a code.

"ZIP Code" (Zone Improvement Program Code) is the (now expired) servicemark of the postal codes used by the United States' Postal Service (USPS). A Zip Code is therefore a postal code for a U.S. address.

If you are interested in the difference between the U.S. and Canadian postal codes--

Zip code: (from Wikipedia)

The first digit represents a certain group of US states.

The second and third digits together represent a region in that group (or perhaps a large city).

The fourth and fifth digits represent a group of delivery addresses within that region.

Canadian postal code: (from Wikipedia) The format is letter-number-letter, space, number-letter-number. The first three characters are called the Forward Sortation Area (FSA). The last three characters are called the Local Delivery Unit (LDU).

FSA

The first letter represents one of 18 regions in Canada.

The number is a 0 for a rural area, and any other digit for an urban area.

The second letter represents a specific rural region, entire medium-sized city, or section of a major metropolitan area.

LDU

Represents a specific single address or range of addresses, which can correspond to an entire small town, a significant part of a medium-sized town, a single side of a city block in larger cities, a single large building or a portion of a very large one, a single (large) institution such as a university or a hospital, or a business that receives large volumes of mail on a regular basis.

LDUs ending in zero correspond to postal facilities, from post offices and small drugstore retail postal outlets all the way up to sortation plants. In urban areas, LDUs may be specific postal carriers' routes. In rural areas where direct door-to-door delivery is not available, an LDU can describe a set of post office boxes or a rural route.