There is another fundamental difference: Advertising is telling consumers how great you are, and publicity is a third party (usually some media outlet) singing your praises.
The relative impact and objective of each are very different.
Public relations can benefit over time from—and is designed to work in conjunction with—advertising and specific marketing initiatives.
The primary focus of public relations is on the credentials of the medium and the quality of the news value. Because PR usually involves having the media cover a story, these stories can live on long past the immediate impact of advertising.
When assessing the monetary value of publicity, many public relations professionals use a simple equation to put a dollar value on a specific placement. This value is determined by first knowing the advertising value.
Advertising values are largely determined by the reach of a specific medium. This is why a 30-second TV commercial on a local broadcast would be a fraction of the cost of a prime-time national rotation.