You have developed a mental image — a summary of information, feelings and experiences — for each business you interact with. That mental summary is called a “brand.” Everyone who interacts with your business, including customers, employees, vendors and people who see your ads, builds a mental picture of your business. That picture is slightly different for each person. Brands change over time, and they can be either positive or negative at any given moment.
Branding activities include everything a business does to generate a brand, from advertising campaigns and web sites to interior design and in-person communication between employees and customers. One shoe store may create a luxurious in-store experience while another may place large numbers of boxes next to sale signs: branding is the work done to create these two different experiences.
Communications include everything a company says to everyone it interacts with, including both marketing communications and interpersonal communications. This includes everything that someone sees or hears: a billboard, a website, an email sent by someone on your staff, and what a cashier says to a customer.
A marketing activity is any specific communications activity designed to achieve a specific goal. Marketing activities are often focused on a specific audience and usually occur over a defined duration. These activities include advertising campaigns, sales events, new product launches and the opening of new locations.
The "offering" is everything that a company offers — all products, all services and all communications. The includes products and services, but also includes the communications that distinguish those goods and services from similar offerings in the marketplace. Two different car dealerships both sell cars and trucks, but one offers Ford brand vehicles and the other offers Toyota brand vehicles. They sell similar products, but their offerings are different. It is the communications — the signs, the logos on the cars, the brochures and websites — that distinguish these two offerings in the minds of consumers.
Please note: the words above are used in different ways by different people. The definitions for these words, provided in the posts linked to above, will be used consistently throughout this site, but may not be defined the same way on other sites or in other publications.