Hi Andrea —
My point with those examples is that given a similar set of circumstances, different innovators can choose to focus on different contexts and get the underlying job(s) done in different ways — yielding different solutions.
Innovation never happens in a vacuum and good ideas can come from anywhere (https://www.linkedin.com/pulse/where-do-ideas-come-from-ash-maurya/). The danger is limiting one’s self to a single solution/category box.
As to biz model canvas vs lean canvas, one should choose the paradigm that fits one’s own mental model. I still find most new products (innovation) struggle with shaky customer/problem/solution assumptions.
But as to your direct question, people don’t generally need a canvas to outline the business they’re already in… and if it truly is a competitive advantage, list it in the unfair advantage box.