I talk a lot about facilitating self-organising teams. For a Scrum Master, a little more than facilitation skills and authority for the process is needed to ensure people interact with professionalism and demonstrate the right behaviours - respect, humility, empathy - at all times.
In most organizations, a Scrum Master is actually a manager and, sometimes, a Scrum Master has to step in when people 'misbehave', but the objective is really to help a team manage itself. The challenge for a Scrum Master is to develop a demeanor that hints at authority just enough to keep people true while giving them freedom. The question is how does someone develop such a demeanor?
I think what you say and how you say it plays a part. As does what you do and how you do it. But 'you' are the core. By that I mean you act by your values and are guided by your principles. And what drives you as a person determines the style in which you conduct yourself. This is what people see.