Charisma and Persuasive are two different with similar outcomes. One might think of charisma as charming or someone having the ability to charm or sweet talking to get their way. The reason I used sweet talking is because sometimes people will say whatever they need to get what they want. Not fussing or complaining to get their way but rather using their outgoing personality or flattery to cause people to want to be around them. Persuasive may get the same results as charisma but its technique is different or rather the approach is different. Persuasive tends to be a little forceful. Although someone might not totally agree with you or want to be around you, your ability to lure or sway would cause them to respond to you in a positive manner. For example, there have been times that I had my mind made up that I wasn't going to do something but because someone paints a picture of its the best thing I tend to go along with it. I have one niece who loves to eat at Olive Garden, she will paint this picture of why we need to go and I don't want to go. Somehow, she always win. She's persuasive and charismatic about her favorite restaurant.
Having this skill is important in business communication because you will be able to meet a vast number of people and build a lasting business relationship and even some personal relationship which are both important to any business.
One person I believe who have this skill is President Obama. He was able to I think persuade the people to trust in themselves and believe that they can have change. His beautiful smile and constant reassuring of their ability to have what they want allowed him to serve two terms.
The other is Michelle Obama. Michelle's ability to lead by example caused many American's to think healthy and take their health serious. She planted gardens and had healthier foods instituted into the schools.