2. Branding = things you do specifically with intent to build a certain image. A good way to imagine this is a high-schooler trying to be part of the "popular" crowd.
3. Advertising = using words and images to make people feel positive about your brand. The most direct way to build one. Language and image tend to be broad and vague to convey a concept that can be interpreted. Ads for Swiffer are a great example.
4. Marketing = anything you do to sell your stuff (including product placement, events, social media, brochures, direct sales - the sky's the limit). Normally marketing activities are targeted to a specific and relatively short-term goal, such as a developer trying to sell a lot of newly constructed homes. Therefore, the language tends to be concrete.
5. Public relations = anything you do to improve your reputation. PR is fundamentally different from other brand-building tools because it relies on conveying factual good news rather than inventing anything. For example, you sponsor a charity run and do a press release. You are broadcasting the truth. The need for credibility is why PR folks seek out the media to "tell the story" for them, rather than relying on press releases to do so.