Brand loyalty is directly linked with brand equity. Brand loyalty is the consumer's commitment to repurchase the products of a specific brand while brand equity refers to the marketing effects which a product results because of the brand name attached with it. The higher the brand equity the higher is the brand equity. This means that people will always show more brand loyalty a specific brand if the brand equity of the product is higher.
Brand loyalty means the consumer loyal to the particular product. But the brand equity means particular brand.