In essence, we can all agree (I think) that branding is all about creating differences. My question then would be : are brands creating consumer differences via digital or they're just using digital as another communication channel?

Customer based brand equity is the differential effect that brand knowledge has on consumer response to the marketing of that brand. A brand has a positive customer based brand equity when consumers react more favorable to a product and the way it is marketed when the brand is identified than when it is not (eg. when a product is attributed to a fictious name or is unnamed) (Strategic Brand Management, K.L.Keller, Pearson 2013).

Basically, the Customer Based Brand Equity occurs when the consumer has a high level of awareness and familiarity with the brand and holds some strong, favorable and unique brand associations in memory. These are also more known as Brand Awareness and Brand Image concepts which I won't elaborate further but will include one more concept of Brand Positioning which is essential to this discussion. Basically, Brand Positioning sets the stage and frame of reference for activities that aim to build Brand Awareness and Brand Image. Brand Positioning is established through definition and communication of the competitive frame of reference which influences the type of creation of both points-of-parity (POP associations) and points-of-difference (POD) associations.

Points of Difference associations are the unique attributes or benefits that consumers strongly associate with a certain brand, positively evaluate, and believe that they could not find to the same extent with a competitive brand. These can be either functional or abstract - imagery related associations. Points of Parity on the other side are those associations that are not necessarily unique to the brand but may in fact be shared with other brands and serve as a necessary vehicle to enable legitimate and credible product offering within a certain category.