Brand loyalty is the consumer's commitment to repurchase the brand and they often help in a lot of positive word of mouth for the brand.
Brand stickiness on the other hand is the repurchase behavior shown by the customers due to the absence of viable alternatives or due to the fear of trying a new brand.
This is often the case of a rural consumer who does not easily switch brands due to the fear associated with it and hence marketers should carefully decode the spurious loyalty from the actual loyalty and work towards ensuring that the customers are not sticking to the brand but are actually loyal.