What do you consider to be the difference between marketing and publicity?

Publicity (i.e., advertising) is part of marketing, which includes other activities such as sales techniques, business communication, and other business developments, as explained here.

You can use publicity to market your product or service…

Marketing is all about sales. Publicity is all about awareness.

To me, it’s about intent. Marketing is always intentional, while publicity can be completely beyond your control.

PR is the placement of stories and mentions about a company or its products in the media with no money exchanging hands. (Other than what you pay the PR firm for the work.)

Marketing is paid campaigns designed to get the word out about your company or product. PR is a function of a company’s marketing efforts. Marketing also include SEO and SEM direct mail, advertising (another subset of a company’s marketing efforts).

Marketing is the planning of, and steps taken, to bring merchants and consumers together. Publicity provides a story about something to attract attention. Publicity is a step in the marketing process.