The only difference that brand management and luxury brand management have is that in case of luxury brand management there is a narrow market to target and branding of only premium products is focused on while brand management is about the branding of any good be it a normal good or a luxurious product. The courses for both are almost the same but for being a luxury brand manager you need to have a specific degree or a certification in luxury brand management. A person with a degree in brand management cannot be hired for the post of luxury brand management but with a poor but a person with a luxury brand management degree can be hired for a capacity of brand manager.