Advertising can:
Help build an image;
Create and foster credibility;
Secure potential customers;
Provide leads, responses, and inquiries;

Advertising cannot:
Force people to contact a company or organization;
Solely sell a product or service;
Guarantee business;
Create customer relationships.

Publicity can:
Establish a company or organization as an authority in their industry;
Enhance company or organization credibility;
Craft an emotional bond with the public;
Tell the inside story;
Set a company or organization apart from competitors;
Generate additional publicity;
Generate and increase response rates;

Publicity cannot:
Be consistently controlled;
Solely accomplish goals.

Although both advertising and publicity are used separately as part of company or organization public relations, advertising and publicity can be combined to create effective public relations synergy.

Publicity Advertising
Companies and organizations normally have little control over the type of publicity generated about them. Publicity however, whether positive or negative, can become a useful tool in terms of advertising. For example:

Celebrity Jessica Simpson garnered nationwide prominence and ridicule when, on her reality television show, she wondered aloud if "Chicken of the Sea" brand tuna fish was actually chicken or tuna. The media portrayed her as a dim-witted entertainer and she became popular public fodder. However, later that year, she begun endorsing a brand of breath mints called "Liquid Ice." In the product's television commercial, Simpson parodies her reality show confusion by debating whether the mint is actually liquid or ice.

Jessica Simpson's initial national embarrassment was intelligently utilized and transformed into a lucrative endorsement deal as a result of combining (bad) publicity with advertising.

Additional examples of using publicity to as a means of adverting inlcude positive product reviews and magazine awards and/or nominations.

Advertising Publicity
Conversely, publicity generated from company or organization advertisements can have powerful and possibly effective outcomes. For example:

The fast food company Carl's Jr./Hardees created an advertisement for the unveiling of a new burger starring celebrity Paris Hilton. The advertisement was aired on television and on the fast food giant's website, and featured Hilton in a bathing suit, washing a car and eating the new burger in a titillating manner. Publicity generated by the commercial showcased the shocking nature of the sexually-charged commercial, which had many Carl's Jr./Hardees customers in an uproar. The Carl's Jr./Hardees website was visited by millions of people as a result of intense media publicity.

Because the nature of the commercial was "shocking", newspapers and news stations were quick to spread publicity. This publicity generated exponential exposure for the company, and millions of people visited the Carl's Jr./Hardees website to view the "shocking" commercial. Although the commercial placed the fast food company in the public's eye, the advertising decision generated negative publicity, and alienated many of Carl's Jr./Hardees' largest income-generating customer base, which is families.

Advertising publicity is however, not always a result of negative publicity. Celebrity endorsements, humorous commercials, and philanthropic causes all have the potential to generate positive publicity.

Links:

http://www.101publicrelations.com/blog/advertising_for_the_pr_of_it_how_to_get_publicity_from_your_advertising_001800.html

http://www.publicrelationsideas.com/publicity/