Five digits first, four more when precision matters
The public-facing ZIP Code most people memorize is five digits. ZIP+4 appends a hyphen and four more (for example, 10001-1234). USPS Postal Facts describes ZIP+4 as improving delivery efficiency by narrowing the sort down from the Post Office to a carrier route segment.
The add-on does not change which city name USPS prints on the last line. If a platform shows the wrong city while the five-digit ZIP is correct, that is a preferred place-name issue, not a missing Plus-4 problem. See why a ZIP code can show the wrong city.
What the four extra digits represent
USPS groups the nine digits as ZIP5 + ZIP4. The first two of the extension often identify a sector (a geographic slice of the ZIP), and the last two identify a segment within that sector (a block, a building, or a PO Box group). Exact assignments change when routes are redrawn, which is why copying a neighbor's Plus-4 is risky.
Large cities with dense blocks benefit most. NYC carriers handle hundreds of delivery points inside a single five-digit ZIP in Manhattan; Plus-4 helps presort mail before it hits the route. The New York ZIP codes guide lists borough-level counts without inventing per-building codes this site has not verified.
ZIP+4 is not an area code extension
Forms sometimes place ZIP and phone fields side by side. The Plus-4 extension belongs only to USPS addressing. Telephone numbers use a separate three-digit area code and seven-digit local number under the North American Numbering Plan.
For the full contrast, read ZIP code vs area code. NYC phones add another layer: Manhattan's 212 family and outer-borough 718 overlays do not correspond to ZIP prefixes such as 100xx or 112xx. The NYC area code guide covers that phone map.