Embedded
It is where the symbol bears resemblance to the product.
Example: An example of this would be NBA logo where it resembles the actual sport: basketball.
Index
A sign or symbol is connected through the product by its similar properties.
Example: is Apple Computers it's logo is an actual Macintosh apple with a bite taken out of it.
Association
For Association we associate the product's image as a whole and connect it to their product. We also take into consideration what we think about ourselves if we use the product.
Example: I regard Armani Exchange as an association with myself. What is that Association?
The brand image to me is stylish, urban and neo-high class and how this works in advertising is surprisingly well, especially for clothing brands. Think of Lacoste compared to Lifted Research Group clothing line. One has established itself as european prep image and the other hip hop streetwear underground clothing line. In advertising the use of semiotics is profoundly potent.
To follow up, the Triad of Semiotics is the Object, Sign and Meaning.
Object: the object represents the actual brand
Sign: what kind of visuals or symbols is used to connect the brand
Meaning: how does the viewer interpret the message?
So for instance, Nestle Quik or Nesquik (Object) uses the chocolate bunny (Sign) in order to have the consumer instantly recognize and connect the chocolate bunny with nestle chocolate milk syrup (Meaning).
