Brand new, at least in my eyes, has two different possible meanings.
The phrase "Brand new" can be defined either as a product of a new brand, or a new product of an already existing brand. Both meanings could be used simultaneously when referring to a product of a new brand, since that product would also technically be a new product, unless of course the product the new brand creates was already a product a different brand already created.
Are both meanings correct? Can both be used interchangeably to describe any new product? Are there more meanings to the phrase "brand new", and is there a possibility that only one of these two definitions of "brand new" is correct?