Within the heads of your many prospective customers, your brand exists . It wont be your red logo, or the tagline on your advertisement, it is the people’s image of your company and your products, and how it impacts their lives.
Therefore, the sum of the decisions you make to influence that image is your Brand Strategy. If you want an image of a low-cost option to the competition, your strategy is to develop lower cost components (buying and creating decisions) and to market your price advantages over your competitors. If the you want an image to focus on great customer support, you might have on-line chat options that is available in your website, an easily-reached or well-trained support department to field questions, and also an advertising campaign that can promote your support advantages to the competitors.
On the other hand, A Marketing Strategy is usually to describe the various advertising/promotional activities you are using to get your message to the audience. The most important part is the part that people see, your ads, coupons and etc.
However, The Brand Strategy, is the part that makes the message that you want to tell others. It is not the most exciting or fun part of the process, but it is the most critical if the process.