Comfort with public speaking and a willingness to claim the spotlight and demand attention seem like necessary traits. Though most of us like attention, not all of us are comfortable in the public eye and not all of us are willing to make people pay attention to us. These traits might seem rather general, but they might be the most obvious connection between the roles/jobs in question.

I don't think that there are similarities.  I agree that actors and musicians need to be creative.  They also need to have charisma.  Senators really don't need that.  They need good interpersonal skills to get along with other senators and be able to persuade them.  They need good speaking skills so they can campaign effectively.  These are really different types of skills/competencies.

I think that creativity is needed for all of these professions, and so is the ability to work in a team.  Senators need to come up with creative solutions to big problems and work with others.  Musicians and actors need to be creative, and usually have to work together.