Don't feel bad if you're grappling with the terms. Even marketing professionals don't always agree on what's what. Here's a brief primer—and we promise, no test later:
brand—"brand" encompasses everything that can be seen, heard, smelled, tasted, touched and experienced about a company
A brand is a distillation of everything about a company: its products, its employees, its actions, the website, packaging, the way company values are expressed, its interaction with the community, how well its brand promise is kept, what your friends have to say about it...you get the idea. An emotional connection is established with the consumer, and based on their experience of the brand, it's consumers—not the company—who ultimately determines what a brand stands for.
visual identity—a company's face to the world
Visual identity (also called identity, corporate identity, visual brand identity, visual branding, and corporate communication) includes corporate colors and fonts, logo application; stationery (business cards, letterhead, envelopes, labels, etc.); print collateral (flyers, brochures, books, annual reports, marketing materials, internal communications); websites; advertising; trade show materials; and signage. These form the visual elements of the brand.
trademark—the simplest form of business identification,
Your trademark is the cornerstone of your visual identity. A great trademark is visual shorthand for everything a company stands for. While it's common to refer to trademarks as logos, for most trademarks (or marks) that's technically not correct. 'Logo' is a shortened version of 'logotype', but a true logotype is a letter-based mark composed of 2 or more letters, like IBM or NBC. Many trademarks combine a logo and graphic mark. For instance, Nike combines their logo and 'swoosh' (a 'mark') to create their trademark.