A brand is how people perceive your company.
Your brand is what people think of when they think about you. It could be a positive image or a negative one. It’s a display of your values, your products, your advertising and at its root, it is the face of your reputation. Your brand is a lot of different things: logos, brochures, websites, business cards, social media profiles, etc. Everything that comes into contact with people becomes the perception of your brand. You ultimately cannot control what people think of your brand, but you must do your best to make the best impression.
An identity is the collection of visual components for your brand.
All of these pieces are identifiers of what your brand is. It makes your brand stand apart from other brands. It is all the elements that make your brand unique. Sometimes we call all of these things brand identities, which include but are not limited to: Logo, colors, fonts, icons, stationary, websites, packaging, clothing, promotional items, social media, email campaigns, signage, and your messages.
A logo is a mark that represents your company.
Your logo is usually the most recognized piece of your branding, its what most people think of when they recall your brand. Many times, people think that their logo must tell the person everything about the company, but its real purpose is to simply be a quick identifier of your company. Apple does not sell fruit, or own any orchards, from what I know, but looking at the logo you can get a sense of who they are, and you certainly wouldn’t forget that simple logo.