Brand Strategy

I was reading about the branding strategy in our marketing book. I came upon some concepts like brand equity, brand sponsorship and brand development. I understood brand equity to be the goodwill or the good image that consumers have for a brand. Suppose if a consumer buys a Gillette Mach 3 Turbo because of its brand name then that is brand equity. I also think that Mach 3 Turbo is a national brand or a manufacturer brand. Furthermore, if we analyze then we see that Gillette indulged in multi-branding when it decided to introduce Mach 3 Turbo into the market after the Mach 3. What do you guys think about my analysis?