Brand identity also goes way beyond visual aspects. Such as social structure, influence, recognition, message, etc.
Authors such as Aaker, Kapferer and Keller have distinct approaches to Brand Identity.
Aaker for example states a fundamental difference when he state that Brand Identity is what the brand should look like in the perspective of the company, not their customers.
It's a very deep concept. But anyway, no author is totally wrong or right in any way. There is a mix of concepts that companies should take further into analysis and state as their identity goal from inside out.