* Advertisement (or advertising): This is *paid* communication. You pay a media outlet (newspaper, television, website, etc.) to present your message to their audience. You have direct control over the message's content, placement, and timing.
* Publicity: This is *earned* communication. It's unpaid media coverage about your company, product, or service. You don't pay for it directly; it arises from news stories, features, reviews, social media mentions, and other forms of media attention. You have less control over the message's content and timing.
Think of it this way: You *buy* advertising, but you *earn* publicity. Both can be very effective, and a good marketing strategy often utilizes both.